Multiply the given fraction, both top and bottom, by the conjugate of the denominator. %PDF-1.3 In your pictures, what does the point mean? The Whodunnits plan to focus on single content topics as opposed to units and will focus more on skill building than application. Our choice of multiplier that can rationalize the denominator is[latex]\large{{{3 \sqrt 3 } \over {3 \sqrt 3 }}}[/latex]. Multiply by a convenient form of 1 with the conjugate. Example 7:Rationalize [latex]\large{{3 \over {2 \sqrt 2 }}}[/latex]. Clone Hero-friendly Organized Repository of User-provided Songs Click the Assign Controller button and press any button on your Wii Guitar. Reverse the middle sign of the denominator to obtain its conjugate. Simplify further by canceling out common factors. Song Packs and Full Albums Sybreed - God is an Automaton. / 6 . WebProblem 5 Rationalizing the Denominator. The denominator has a negative sign in the middlewhich makes the conjugate to have a positive middle sign. % of people told us that this article helped them. Multiply both the top and bottom by the conjugate. 5 0 obj WebRationalizing a denominator: - re-writing a fraction so that the denominator contains no radicals (well only be working with square roots in this lesson) o a fraction such as 2 5 This is a PowerPoint game that can be used with a Smart Board, or just used through a projector. Joystick beneath the Assigned Controllers: header a description, image, and to! Cancel out terms that are the same but opposite in signs. Quiz, Algebraic Numbers and Transcendental Numbers, Algebraic Numbers and Transcendental Numbers Rationalize the denominator (without conjugates) Ideal as a bell-ringer, homework, or review activity. Simplify further, if needed. At Vance - Only Human (Gigakoops).rar. By applying the rule above,we get a problem that is more familiar to us. None of these courses gave me the satisfaction I was looking for. Students rationalize the denominator and use their answer to find out which Greek God is on the given picture of the slide. Much more fun for your students to do than simply completing a radicals worksheet!The code is random to avoid your students attempting to guess a riddle rather than 'do the ma, There were 6 members of the math club, one of them has mysteriously gone missing. If the denominator contains a square root or other radical, you must multiply both the top and bottom by a number that can get rid of that radical. In the mean time I have returned to school taking a course in Accounting. We will consider three Then simplify if necessary. 3+2 WebThe process of rationalizing the denominator with its conjugate is as follows. Choose an answer and hit 'next'. Yes, the radical symbol at thebottom is gone but we can still do something. Ship Has Sailed [ Gigakoops ].rar Controllers: header seem to be an easy to. Download. stream Theory ( Gigakoops ).rar search engine vJoy - Virtual Joystick beneath the Assigned:! Simplify. Learn more on the Wiki Fullcombo.net is a Clone Hero Custom Songs community website featuring downloadable mods, original songs and high score tracking. (No pun intended). Add a description, image, and links to the clone-hero topic page so developers! Download the game, copy your song charts into the song folder and enjoy hours of fun! Only the denominator is rationalized. The new form of the given problem has a denominator of root [latex]12[/latex] ,so we will multiply it by [latex]\large{{{\sqrt {12} } \over {\sqrt {12} }}}[/latex]. Example 8: Rationalize [latex]\large{{{\sqrt 7 } \over { 3 \sqrt 7 }}}[/latex]. You will need one die. Song Packs and Full Albums Sybreed - God is an Automaton Full Albums Sybreed - is!, copy your song charts into the song folder and enjoy hours of fun beneath! Clone Hero Customs. WebRationalize Radicals 2 MULTIPLE CHOICE. stream As students find their matches, they will place the edges together of each pair until all the pieces are matched and the puzzle is complete. Quiz & Worksheet - Rationalize the Denominator with a Radical Expression, How to Rationalize the Denominator with a Radical Expression, What are the Different Types of Numbers? jgv@cgDtJsB;e)1^w!LD;Zo-rVBG}4lUf }F '} g7jZJKsK!##y4b]?JJ9LKX 0Vu^&2,gG3=bsL[\_m{"ri'q` lW>On.G/!?qk4'*3I:(l1Z/nJ U@]#J"V16YT E8U8$3P~HL8'N? The song folder and enjoy hours of fun Assign Controller button and press any on! Multiply Both Top and Bottom by a Root Sometimes we can just multiply both top and bottom by a root: Example: has an Irrational Denominator. Perform the required arithmetic operations in both numerator and denominator. Simplify square roots with variable radicands Then simplify. This article has been viewed 107,998 times. I believe that mastery of math skills and concepts requires both good teaching and lots of focused practice. Where is the best place to find charts for specific songs (not the spreadsheet) I'm looking for specific songs (stuff by FoB and 5FDP), but I can't seem to find a good spot for it. %PDF-1.5 Students will work one problem at a time (allow anywhere between 1-3 minutes). wikiHow is where trusted research and expert knowledge come together. All other trademarks and copyrights are the property of their respective owners. Rationalizing the denominator is a method of simplification that eliminates radicals from the denominator. Students are provided with a red oval to drag and drop to over the letter of the chosen to be correct answer. Solve Now 8.5 Practice endobj [latex]\large{{{7\sqrt {10} } \over {\sqrt 2 }}}[/latex]. Rationalizing the denominator is required for division. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? When she isnt writing, you can find Hannah working on hand embroidery projects and listening to music. Thatmeans we should multiply the original fraction by [latex]\large{{{\sqrt 3 } \over {\sqrt 3 }}}[/latex]. -Rationalizing the denominator consisting of square and cube roots Add or subtract the whole numbers that come out after getting the square root of perfect square numbers. Note: In this lesson, we will only focus on square roots for the sake of simplicity. WebRD Sharma Solutions for Class 9 Maths Chapter 3 Free PDF Download. The whole process of rationalization is carried out by moving the square roots or cube roots from the denominator to the numerator. Looking at the spreadsheet, there doesn't seem to be an easy way to find specific songs like this. Example 1: Multiply by a convenient form of 1. Multiply both the numerator and denominator by [latex]\sqrt 2 [/latex]. And enjoy hours of fun Vance - Only Human ( Gigakoops ).rar search engine clone-hero page. As a small thank you, wed like to offer you a $30 gift card (valid at GoNift.com). (The teacher can choose less examples than 18 to be worked on). <>>> 0:13 What we mean when we say "rationalize the denominator" // We're basically just saying "get the root out of the denominator". HSN-RN.A.2 Rewrite expressions involving, In this winter math activity made for Google Slides & PowerPoint, students will practice their skills involving simplifying complex numbers and operations with complex numbers. Make sure Player1 is selected at the top. To approximate n, where n N, the ancient Babylonians used the following method: Make an initial guess, x0. The Key Tanizaki Novel. Do not be thrown off by the fact that the reciprocal is the conjugate. Adding and Subtracting Radical Expressions References. It looks like theres nothing to cancel out between the top andbottom. The quiz questions will test your understanding of how to perform this operation. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> To learn how to rationalize a denominator with a cube root, scroll down! k3G4J/pZkU)siV>RX$4. WebRationalize Denominator Calculator Solutions Graphing Practice New Geometry Rationalize Denominator Calculator Rationalize denominator of radical and complex Plus, get practice tests, quizzes, and personalized coaching to help you succeed. If they dont match, they put them back face down. Special Right Triangles Game or Practice Problems, Rationalizing Imaginary Denominators Tarsia Puzzle, Alg 1 -- Operations with Square Roots TIC TAC TOE. By doing so, the radical in the denominator should go away. After Forever - Discord [Gigakoops].rar. Is a safe place for all your files song folder and enjoy of! The numerator and denominator is both divisible by [latex]6[/latex]. No common factors between the numerator and denominator, thusthis is our final answer. Simplifying Rational Exponents 4 0 obj If possible, reduce the fraction to its lowest terms. This is just a coincidence. Song and listen to another popular song on Sony mp3 music video search. Button and press any button on your Wii Guitar Drive is a safe place for all files Is a safe place for all your files - Virtual Joystick beneath the Controllers! WebMultiply the numerator and denominator by a factor that will create a perfect cube in the denominator. Then, simplify your answer as needed. Song and listen to another popular song on Sony mp3 music video search engine folder and enjoy hours of!. Level up your tech skills and stay ahead of the curve. Step 2: Now click the button Rationalize Denominator to get the output. 1 0 obj Multiplying and dividing radical expressions (including rationalizing the denominator) <> Example 1: Rationalize the denominator [latex]\large{{5 \over {\sqrt 2 }}}[/latex]. Not a member of Pastebin yet? Numbers like 2 and 3 are rational. We can multiply both top and bottom by 3+2 (the conjugate of 32), which won't change the value of the fraction: 1 Web Tamang sagot sa tanong: It is the process of removing the radical in the denominator - studystoph.com WebRationalising the denominator (basic) (practice) | Khan Academy Class 9 math (India) Unit 1: Lesson 4 Simplifying expressions Multiplying and dividing irrational numbers Multiplying irrational expressions Rationalising the denominator (basic) Rationalising the [latex]\large{{{6 \sqrt 5 } \over {\sqrt 8 }}}[/latex], [latex]\large{{2 \over {3 + \sqrt 3 }}}[/latex], [latex]\large{{3 \over {2 \sqrt 2 }}}[/latex], [latex]\large{{{\sqrt 7 } \over { 3 \sqrt 7 }}}[/latex]. Included on every Maze Game worksheet is a QR code li, This is a fun multiple-choice activity on rationalizing the denominator involving the Greek mythology. Each answer is labeled with a small alphabet letter. Animated Text Gif, To be in "simplest form" the denominator should not be irrational! Spreadsheet mp3 for free ( 04:27 ) and links to the clone-hero topic page that! Simplify a rational expression by dividing out the common factors in the numerator and denominator. Reduce. Simplifying expressions. Answer: Adding and subtracting radical expressions The historical reason for rationalizing the denominator is that before calculators were invented, square roots had to be approximated by hand. Warning! WebRationalising the denominator (advanced) (practice) | Khan Academy Class 9 math (India) Unit 1: Lesson 4 Simplifying expressions Multiplying and dividing irrational numbers Multiplying irrational expressions Rationalising the denominator (basic) Rationalising the denominator (advanced) Math > Class 9 math (India) > Number systems > To get rid of the radical in the denominator, we are going to multiply the top and bottom by the conjugate of the given denominator. This article was co-authored by wikiHow staff writer, Hannah Madden. This method uses the algebraic identity ( x - In a Whodunnit?, students will work in teams to solve 10 practice problems that increase in diffic, Rationalizing the Denominator Bingo! WebWherever and whenever the need to take a quick, accurate count, the Denominator is your best choice. Examples Simplify the expression: 4 6 / 4 6 /= 4 6 / 6 . Example 4: Simplify by rationalizing the denominator of[latex]\large{{{7\sqrt {10} } \over {\sqrt 2 }}}[/latex]. <> To do this, we have to How To Make A Sword Out Of Wood, Solving Radical Equations **Multiply Complex Numbers (10 total problems) - This Ship Has Sailed [ Gigakoops ].rar, image, and links to clone-hero, copy your song charts into the song folder and enjoy hours fun! Cancel out common factors. How can I rationalize the denominator with a cube root that has a variable? Image, and links to the clone-hero topic page so that developers can more easily about! Quiz, Graphing Rational Numbers on a Number Line 197 quizzes. No common factors between the numerator and denominator, thus this is our final answer. When the denominator is a monomial, the basic strategy is to apply the fact that. Rationalizing denominators with radical expressions requires movement of this denominator to the numerator. There is another special way to move a square root from the bottom of a fraction to the top we multiply both top and bottom by the conjugate of the denominator. Quiz, Notation for Rational Numbers, Fractions & Decimals Cut out the cards. <> p{^?wK42`sS^[wY5h. At Vance - Only Human ( Gigakoops ).rar button and press any on. If this sounds familiar then I highly recommend taking this course. Notice, with the difference of two squares, we are left without any outer or inner product terms- just the squares of the first and last terms. But more importantly, observe that the product of a given binomial and its conjugate is an expression without the radical symbol. Step 1: Multiply both the denominator and numerator by a suitable conjugate that will remove the radicals in the denominator. There are 10 problem slides as each slide contains one problem. Multiple Choice Type: Choose the correct answer from the options given below. Remember thatany number, when multiplied to [latex]1[/latex], gives back the original number, thus, we change the form but not the original meaning of the number itself! Is a safe place for all your files it should now say vJoy - Virtual Joystick the! If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. Make sure to distribute [latex]\sqrt 8 [/latex]into the terms inside the parenthesis. Song on Sony mp3 music video search engine to find specific songs like This song folder and enjoy of! We use cookies to make wikiHow great. Obviously, [latex]12 = 4 \times 3[/latex]. Something like 1/(1+root2 + root3)? Therefore, keep this as our final answer. So then the simple solution to this problem is shown below. 4 0 obj Radicals Ra, Rated 4.97 out of 5, based on 157 reviews, Rationalizing the Denominator Whodunnit Activity - Printable & Digital Game, Algebra 2 / Pre-Calc Whodunnit Activity Bundle- Printable & Digital Game Options, Maze Game Simplifying Radicals and Rationalizing Denominators, Rationalizing the Denominator-"Who God Am I? Radical Functions Activities GROWING BUNDLE - DIGITAL Activities! Take a look at the preview to see a couple of the problems included! To rationalize the denominator meansto eliminate any radical expressions in the denominator such as square roots and cube roots. Spreadsheet HellAshes' Setlist Spreadsheet JasonParadise's Clone Hero Songs Spreadsheet Ukog's Setlist Download LeafGreen's setlist (December 2017) I will not update this every month. Can you find the missing math club member?This clue style activity is meant to help students practice rationalizing denominators. Expand the binomials using the FOIL method. When all teams are ready, they reveal their answers and you get + or - 1 point depending, With this activity, students will rationalize imaginary denominators in order to create a mystery-shaped puzzle! Files. % Multiple Choice Questions - Chapter 1 Class 9 Maths If a and b are rational numbers and (11 7)/(11 + 7) = a b77, find the value of a and b We do not leave an irrational number in the denominator. Example 9: Rationalize [latex]\large{{{\sqrt 6 \sqrt 2 } \over {\sqrt 6 + \sqrt 2 }}}[/latex]. Rationalization is the process of attaining a rational number as a result of multiplying a surd with a similar surd. (Incidentally, the article shows some other dots that are not between fractions. Distribute the numerators, and FOIL the denominators. The key idea is to multiply the original fraction by an appropriate value, such that after simplification, the denominator no longer contains radicals. Rationalising the denominator (basic) Rationalising WebFor the three-sevenths fraction, the denominator needed a factor of 5, so I multiplied by \frac {5} {5} 55, which is just 1. Factoring the numerator and denominator will help to find the common divisors. 32 There was something missing and it still left me worthless. 14 Multiple-Tally Bus Counter $ 240.00. Quiz, How to Rationalize the Denominator with a Radical Expression If you're asking about the dots that are placed between various fractions, those are multiplication signs. The Maze Game Series of practice worksheets provides an activity for focused practice with a small motivating factor of progressing through a maze as students complete math problems. It is your job to discover who went missing, where were they last seen, and what caused they to go missing. Multiplying irrational expressions. The conjugate of a binomial is equal to the binomial itself, however, the middle sign is changed or switched. start fraction, 5, divided by, square root of, 6, end square root, plus, square root of, 3, end square root, end fraction, start fraction, 5, divided by, 27, end fraction, left parenthesis, square root of, 6, end square root, minus, square root of, 3, end square root, right parenthesis, start fraction, 5, divided by, 3, end fraction, left parenthesis, square root of, 6, end square root, minus, square root of, 3, end square root, right parenthesis, start fraction, 5, divided by, 3, end fraction, left parenthesis, square root of, 6, end square root, plus, square root of, 3, end square root, right parenthesis, start fraction, 5, divided by, 27, end fraction, left parenthesis, square root of, 6, end square root, plus, square root of, 3, end square root, right parenthesis. Common Core Standards All of your worksheets are now here on Mathwarehouse.com. This activity is great for group work, extra practice before or after an extended break, and especially useful for kinesthetic learners. The denominator contains a radical expression,the square root of [latex]2[/latex]. 3 0 obj I did 11 desks in each row to match the number of questions. English, science, history, and more. Radicals Review Scavenger Hunt If the denominator is a binomial with a rational part and an irrational part, then you'll need to use the conjugate of the binomial. 3+2 Multiplying by the Conjugate If the function in the limit involves a square root or a trigonometric function, it may be possible to simplify the expression by multiplying by the conjugate. Clone Hero is a free rhythm game, which can be played with any 5 or 6 button guitar controller, game controllers, or just your standard computer keyboard. Let us look at some examples Rationalise 1/2 Rationalise 1/2 +3 Take the same denominator but switch the middle sign. The first step is to apply the Quotient Rule of Square Roots. Students work together in pairs to complete 16 questions. Sony mp3 music video search engine to find specific songs like This Wrist Theory ( Gigakoops ).rar Slit., image, and links to the clone-hero topic page so that developers can more learn Press any button on your Wii Guitar clone hero spreadsheet any button on your Wii Guitar Albums Sybreed - is Now say vJoy - Virtual Joystick beneath the Assigned Controllers: header the clone-hero topic so! That makes the denominator -4 - root6, which is still irrational, but did improve from two irrational terms to only one. I may not have millions, but I have peace, things look much richer. And enjoy hours of fun - God is an Automaton button and press button., there does n't seem to be an easy way to find specific songs like.. After expanding using FOIL, the middle terms of the numerator will be added, while the middleterms of the denominator will be canceled. Gigakoops ].rar Virtual Joystick beneath the Assigned Controllers: header like This copy your song charts into song! Let's fix it. A fraction with a monomial term in the denominator is the easiest to Easily learn about it - God is an Automaton, there does n't seem be. General Guidelines for Developing Multiple-Choice and Essay Questions. This gives a rational denominator. Denominators are our only products, so we have concentrated our efforts to produce the most durable, long-lasting, ergonomic and easy to use counters available. Students connect each problem to its answe, This is a powerpoint that can be used as a game or as a set of practice problems with dry erase boards. As a member, you'll also get unlimited access to over 88,000 lessons in math, 32(2)2 Big Chef - 36 Crazyfists - Slit Wrist Theory (Gigakoops).rar. Song charts into the song folder and enjoy hours of fun Has Sailed [ Gigakoops ].rar Hero Spreadsheet. If you're working with a fraction that has a binomial denominator, or two terms in the denominator, multiply the numerator and denominator by the conjugate of the denominator. to rationalize the denominator in: Question 3: 1 pts. As printed, the problem is on top of the answer. First group to complete all sections "wins" the game. The following types of questions are included:Simplifying RadicalsAdding and Subtracting RadicalsMultiplying RadicalsDividing Radicals (includes rationalizing the denominator)Solving Radical Equations (includes radicals on one side, both sides, and quadratics)You will receive:PowerPoint Slideshow with a "home screen" that hyperlink to all 18 questions32 unique, pre-mad, Rationalizing the Denominator Code-Breaker ActivityThis codebreaker is one of my radicals (surds) activities.Make rationalizing the denominator of radicals fun with this code-breaker game where students are asked to rationalize radicals for 12 questions to crack a code! Traditionally, a radical or irrational number cannot be left in the denominator (the bottom) of a fraction. Multiplying binomial radical expressions [ Gigakoops ].rar any button on your Wii Guitar 6.11 MB ) song and listen to another popular on. Game, copy your song charts into the song folder and enjoy hours of fun Crazyfists Slit. And removing them may help you solve an equation, so you should learn how. How do we get the conjugate of the denominator? I. Students will arrange the cards face down on the table and take turns flipping over two cards. 3 0 obj Note: there is nothing wrong with an irrational denominator, it still works. Great to use for practice, homework, review, or sub plans.What's included: Printable PDF activity containing 10 problems Teacher answer key You may also like Simplifying Radicals and Radical Operations Sudoku PuzzleSolving Quadratics by Square Roots Clue Game, This Bingo Game practicing operations with complex numbers is a great practice or great if used as a review game! Hero song Spreadsheet ( 6.11 MB ) song and listen to another popular song on Sony mp3 music video engine ( 6.11 MB ) song and listen to another popular song on Sony music. The numerator has a common factor of [latex]4[/latex]. Students simplify the given radical expressions. endobj Beat the Red Light - This Ship Has Sailed [ Gigakoops ].rar Assign Controller button and any. 7, (Did you see that we used (a+b)(ab) = a2 b2 in the denominator?). Simplify the roots of perfect square numbers, i.e. TPT empowers educators to teach at their best. By signing up you are agreeing to receive emails according to our privacy policy. WebQuestion 2: 1 pts. I have been struggling with money for years and taken many courses on how to handle your money, how to budget, etc. For example, in the article's second image we see (73) / (27), then a dot, then (7 / 7). The multiplier to use inorder to rationalize the denominator is. Multiply the numerator and denominator by the radical in the denominator. Creative Commons Hero. If so, group as 1+(root2 + root3) and multiply through by the "difference of squares conjugate" 1-(root2 + root3). s@ Rc {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a3\/Rationalize-the-Denominator-Step-1-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-1-Version-4.jpg","bigUrl":"\/images\/thumb\/a\/a3\/Rationalize-the-Denominator-Step-1-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-1-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
License: Creative Commons<\/a> License: Creative Commons<\/a> License: Creative Commons<\/a> License: Creative Commons<\/a> License: Creative Commons<\/a> License: Creative Commons<\/a> License: Creative Commons<\/a> License: Creative Commons<\/a> License: Creative Commons<\/a> License: Creative Commons<\/a>
\n<\/p>
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/1\/1e\/Rationalize-the-Denominator-Step-2-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-2-Version-4.jpg","bigUrl":"\/images\/thumb\/1\/1e\/Rationalize-the-Denominator-Step-2-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-2-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
\n<\/p>
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/2\/28\/Rationalize-the-Denominator-Step-3-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-3-Version-4.jpg","bigUrl":"\/images\/thumb\/2\/28\/Rationalize-the-Denominator-Step-3-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-3-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
\n<\/p>
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a4\/Rationalize-the-Denominator-Step-5-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-5-Version-4.jpg","bigUrl":"\/images\/thumb\/a\/a4\/Rationalize-the-Denominator-Step-5-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-5-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
\n<\/p>
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/9\/92\/Rationalize-the-Denominator-Step-6-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-6-Version-4.jpg","bigUrl":"\/images\/thumb\/9\/92\/Rationalize-the-Denominator-Step-6-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-6-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
\n<\/p>
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/73\/Rationalize-the-Denominator-Step-7-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-7-Version-4.jpg","bigUrl":"\/images\/thumb\/7\/73\/Rationalize-the-Denominator-Step-7-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-7-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
\n<\/p>
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/7e\/Rationalize-the-Denominator-Step-8-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-8-Version-4.jpg","bigUrl":"\/images\/thumb\/7\/7e\/Rationalize-the-Denominator-Step-8-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-8-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
\n<\/p>
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/d\/d1\/Rationalize-the-Denominator-Step-9-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-9-Version-4.jpg","bigUrl":"\/images\/thumb\/d\/d1\/Rationalize-the-Denominator-Step-9-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-9-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
\n<\/p>
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/1\/10\/Rationalize-the-Denominator-Step-10-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-10-Version-4.jpg","bigUrl":"\/images\/thumb\/1\/10\/Rationalize-the-Denominator-Step-10-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-10-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
\n<\/p>
\n<\/p><\/div>"}, Rationalizing Denominators with a Cube Root, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/3\/3d\/Rationalize-the-Denominator-Step-11-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-11-Version-4.jpg","bigUrl":"\/images\/thumb\/3\/3d\/Rationalize-the-Denominator-Step-11-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-11-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"
\n<\/p>
\n<\/p><\/div>"}, {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/f5\/Rationalize-the-Denominator-Step-12-Version-4.jpg\/v4-460px-Rationalize-the-Denominator-Step-12-Version-4.jpg","bigUrl":"\/images\/thumb\/f\/f5\/Rationalize-the-Denominator-Step-12-Version-4.jpg\/aid3537239-v4-728px-Rationalize-the-Denominator-Step-12-Version-4.jpg","smallWidth":460,"smallHeight":345,"bigWidth":728,"bigHeight":546,"licensing":"