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2026-01-01
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<p>505 Learners</p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>The square root is the number obtained when a number is multiplied with itself. We apply the concept of square root in architecture, to measure volume and surface area. In this article, we’ll learn how to find the square root of 120.</p>
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<p>The square root is the number obtained when a number is multiplied with itself. We apply the concept of square root in architecture, to measure volume and surface area. In this article, we’ll learn how to find the square root of 120.</p>
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<h2>What is the Square Root of 120</h2>
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<h2>What is the Square Root of 120</h2>
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<p>The<a>square</a>root<a>of</a>120 is 10.954. Finding the square root of a<a>number</a>is the inverse process of finding the<a>perfect square</a>. The square root of 120 is written as √120. </p>
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<p>The<a>square</a>root<a>of</a>120 is 10.954. Finding the square root of a<a>number</a>is the inverse process of finding the<a>perfect square</a>. The square root of 120 is written as √120. </p>
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<h2>Finding the square root of 120</h2>
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<h2>Finding the square root of 120</h2>
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<h3>Square root of 120 using prime Factorization Method</h3>
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<h3>Square root of 120 using prime Factorization Method</h3>
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<p>The prime factorization of 120 breaks 120 into its<a>prime numbers</a>. </p>
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<p>The prime factorization of 120 breaks 120 into its<a>prime numbers</a>. </p>
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<p>The numbers 2, 3, and 5 are the prime numbers .</p>
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<p>The numbers 2, 3, and 5 are the prime numbers .</p>
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<p>Prime factorization of 120 is 23 × 31× 51.</p>
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<p>Prime factorization of 120 is 23 × 31× 51.</p>
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<p>Since 2 is repeating, we should pair them. We can’t pair 3 and 5 because they are not repeating.</p>
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<p>Since 2 is repeating, we should pair them. We can’t pair 3 and 5 because they are not repeating.</p>
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<p>Therefore, √20 is expressed as 2x√2 x √3 x√5, the simplest radical form.</p>
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<p>Therefore, √20 is expressed as 2x√2 x √3 x√5, the simplest radical form.</p>
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<h3>Square root of 120 using long division method</h3>
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<h3>Square root of 120 using long division method</h3>
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<p>The long<a>division</a>method finds the square root of non-perfect squares.</p>
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<p>The long<a>division</a>method finds the square root of non-perfect squares.</p>
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<p>The long division method finds the square root of non-perfect squares.</p>
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<p>The long division method finds the square root of non-perfect squares.</p>
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<p><strong>Step 1:</strong>Write down the number 120</p>
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<p><strong>Step 1:</strong>Write down the number 120</p>
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<p><strong>Step 2:</strong> Number 120 is a three-digit number, so pair them as (1), (20)</p>
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<p><strong>Step 2:</strong> Number 120 is a three-digit number, so pair them as (1), (20)</p>
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<p><strong>Step 3:</strong>Find the largest that is closest to the first pair (1), which is 12</p>
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<p><strong>Step 3:</strong>Find the largest that is closest to the first pair (1), which is 12</p>
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<p><strong>Step 4:</strong>Write down 1 as the<a>quotient</a>, which will be the first digit of the square root.</p>
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<p><strong>Step 4:</strong>Write down 1 as the<a>quotient</a>, which will be the first digit of the square root.</p>
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<p><strong>Step 5:</strong>Subtracting 12 from 1 will leave zero as the<a>remainder</a>. Now bring down the second pair (20) and place it beside 0.</p>
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<p><strong>Step 5:</strong>Subtracting 12 from 1 will leave zero as the<a>remainder</a>. Now bring down the second pair (20) and place it beside 0.</p>
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<p><strong>Step 6:</strong>Now double the quotient you have, that is multiply the quotient 1 with 2 and the result will be 2</p>
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<p><strong>Step 6:</strong>Now double the quotient you have, that is multiply the quotient 1 with 2 and the result will be 2</p>
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<p><strong>Step 7:</strong>Choose a number such that it can be placed after 2. The two-digit number created should be<a>less than</a>the second pair (20). Here, we place 0 after 2, because the number formed will be<a>greater than</a>20.</p>
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<p><strong>Step 7:</strong>Choose a number such that it can be placed after 2. The two-digit number created should be<a>less than</a>the second pair (20). Here, we place 0 after 2, because the number formed will be<a>greater than</a>20.</p>
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<p><strong>Step 8:</strong>Subtract 0 from 20 → 20-0 =20. Now add a<a>decimal</a>point after the new quotient and adding two zeros will make it 2000</p>
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<p><strong>Step 8:</strong>Subtract 0 from 20 → 20-0 =20. Now add a<a>decimal</a>point after the new quotient and adding two zeros will make it 2000</p>
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<p><strong>Step 9:</strong>Apply step 7 over here and continue the process until you reach 0.</p>
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<p><strong>Step 9:</strong>Apply step 7 over here and continue the process until you reach 0.</p>
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<p>Step 10: We can write √120 as 10.954 </p>
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<p>Step 10: We can write √120 as 10.954 </p>
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<h3>Square root of 120 by Approximation method</h3>
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<h3>Square root of 120 by Approximation method</h3>
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<p>The approximation method finds the estimated square root of non-perfect squares.</p>
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<p>The approximation method finds the estimated square root of non-perfect squares.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect square to 120. Numbers 100 and 121 are the closest perfect square to 120.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect square to 120. Numbers 100 and 121 are the closest perfect square to 120.</p>
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<p><strong>Step 2:</strong>We know that √100 = 10 and √121 = 11. Thus, we can say that √120 lies between 10 and 11.</p>
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<p><strong>Step 2:</strong>We know that √100 = 10 and √121 = 11. Thus, we can say that √120 lies between 10 and 11.</p>
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<p><strong>Step 3:</strong>Check if √120 is closer to 10 or 11. Let us take 10.5 and 11. Since (10.5)2 is 110.25 and (11)2 is 121, √120 lies between them.</p>
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<p><strong>Step 3:</strong>Check if √120 is closer to 10 or 11. Let us take 10.5 and 11. Since (10.5)2 is 110.25 and (11)2 is 121, √120 lies between them.</p>
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<p><strong>Step 4:</strong>We can keep changing the values of 10.5 to 10. 6 and iterate the same process without changing 12 as the closest perfect square root.</p>
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<p><strong>Step 4:</strong>We can keep changing the values of 10.5 to 10. 6 and iterate the same process without changing 12 as the closest perfect square root.</p>
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<p>The result of √120 will be 10.954 </p>
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<p>The result of √120 will be 10.954 </p>
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<h2>Common Mistakes and How to Avoid Them in Square Root of 120</h2>
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<h2>Common Mistakes and How to Avoid Them in Square Root of 120</h2>
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<p>Take a look at mistakes a child can make while finding the square root of 120:</p>
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<p>Take a look at mistakes a child can make while finding the square root of 120:</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Find the value of (√120)⁴</p>
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<p>Find the value of (√120)⁴</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Value of (√120)4 = 14115.8 </p>
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<p>Value of (√120)4 = 14115.8 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>(√120)4 = √120 x √120 x √120 x √120 = 10.9 × 10.9 × 10.9 × 10.9 = 14115.8 </p>
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<p>(√120)4 = √120 x √120 x √120 x √120 = 10.9 × 10.9 × 10.9 × 10.9 = 14115.8 </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>Calculate the perimeter of the square having an area of 120 square units</p>
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<p>Calculate the perimeter of the square having an area of 120 square units</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Perimeter of the square = 43.817 </p>
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<p>Perimeter of the square = 43.817 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Square has 4 sides. So, the length of each side is √120. To find the perimeter of a square, multiply 4 with √120 → 4 x √120 = 43.817 </p>
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<p>Square has 4 sides. So, the length of each side is √120. To find the perimeter of a square, multiply 4 with √120 → 4 x √120 = 43.817 </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>What is the value of √119 and √120 when added together?</p>
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<p>What is the value of √119 and √120 when added together?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The sum of √119 and √120 is 21.862 </p>
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<p>The sum of √119 and √120 is 21.862 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>√119 is 10.908 and √120 is 10.954. So, adding √119 and √120 will give the sum of 21.862 </p>
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<p>√119 is 10.908 and √120 is 10.954. So, adding √119 and √120 will give the sum of 21.862 </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>If x = √120, what is the value of x²?</p>
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<p>If x = √120, what is the value of x²?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The value of x2 = 120 </p>
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<p>The value of x2 = 120 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>When the square root gets squared, the root gets canceled. Here, x = √120 and x2 = (√120)2 = 120. </p>
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<p>When the square root gets squared, the root gets canceled. Here, x = √120 and x2 = (√120)2 = 120. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on 120 Square Root</h2>
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<h2>FAQs on 120 Square Root</h2>
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<h3>1.Why is 120 not a perfect square?</h3>
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<h3>1.Why is 120 not a perfect square?</h3>
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<p>120 is not a perfect square because no number is multiplied by that number itself to give 120 as the<a>product</a>. </p>
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<p>120 is not a perfect square because no number is multiplied by that number itself to give 120 as the<a>product</a>. </p>
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<h3>2.What number is closest to √120?</h3>
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<h3>2.What number is closest to √120?</h3>
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<p>The √120 is closer to √100 and √121. The values of √100 and √121 are 10 and 11 respectively. </p>
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<p>The √120 is closer to √100 and √121. The values of √100 and √121 are 10 and 11 respectively. </p>
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<h3>3.Is √120 irrational?</h3>
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<h3>3.Is √120 irrational?</h3>
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<h3>4.What is √120 simplified?</h3>
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<h3>4.What is √120 simplified?</h3>
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<p>√120 is simplified using the long division method. Using this method, √120 simplified will be 10.954 </p>
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<p>√120 is simplified using the long division method. Using this method, √120 simplified will be 10.954 </p>
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<h3>5.What is the cube root of 120?</h3>
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<h3>5.What is the cube root of 120?</h3>
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<p>The<a>cube</a>root of 120 is 4.932 </p>
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<p>The<a>cube</a>root of 120 is 4.932 </p>
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<h2>Important Glossaries for Square Root of 120</h2>
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<h2>Important Glossaries for Square Root of 120</h2>
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<ul><li><strong>Perfect Square:</strong>Product obtained when the same number gets multiplied twice</li>
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<ul><li><strong>Perfect Square:</strong>Product obtained when the same number gets multiplied twice</li>
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</ul><ul><li><strong>Approximate Value:</strong>Value closer to the exact number</li>
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</ul><ul><li><strong>Approximate Value:</strong>Value closer to the exact number</li>
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</ul><ul><li><strong>Prime Factorization:</strong>Breaking down the number into its prime factors.</li>
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</ul><ul><li><strong>Prime Factorization:</strong>Breaking down the number into its prime factors.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>