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2026-01-01
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<p>413 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>Having an understanding of the concept of cube root is essential in the fields of engineering, construction and science. Cube roots are also used to measure volumes in three-dimensional spaces on a daily basis. Let us now learn about the cube root of 108.</p>
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<p>Having an understanding of the concept of cube root is essential in the fields of engineering, construction and science. Cube roots are also used to measure volumes in three-dimensional spaces on a daily basis. Let us now learn about the cube root of 108.</p>
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<h2>What is the cube root of 108?</h2>
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<h2>What is the cube root of 108?</h2>
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<p>∛108 = 4.762203. </p>
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<p>∛108 = 4.762203. </p>
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<p>We can arrive at the<a>cube</a>root<a>of</a>a given<a>number</a>using; </p>
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<p>We can arrive at the<a>cube</a>root<a>of</a>a given<a>number</a>using; </p>
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<ul><li>Halley’s method - Use of approximation to find the cube root </li>
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<ul><li>Halley’s method - Use of approximation to find the cube root </li>
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</ul><ul><li>Prime factorization - we break 108 into its<a>prime factors</a>to find the cube root </li>
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</ul><ul><li>Prime factorization - we break 108 into its<a>prime factors</a>to find the cube root </li>
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</ul><ul><li>Estimation method - we analyze the given number between two known<a>perfect cubes</a>. Let us now learn in detail; </li>
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</ul><ul><li>Estimation method - we analyze the given number between two known<a>perfect cubes</a>. Let us now learn in detail; </li>
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</ul><h3>Cube root of 108 by Halley’s method</h3>
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</ul><h3>Cube root of 108 by Halley’s method</h3>
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<p>Halley’s method is a proven effective method for finding the<a>cube root</a>of a number. We use the below<a>formula</a>; </p>
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<p>Halley’s method is a proven effective method for finding the<a>cube root</a>of a number. We use the below<a>formula</a>; </p>
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<p>∛a≅ x((x3+2a) / (2x3+a))</p>
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<p>∛a≅ x((x3+2a) / (2x3+a))</p>
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<p>In the formula; </p>
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<p>In the formula; </p>
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<p>a = given number, 108 </p>
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<p>a = given number, 108 </p>
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<p>x =<a>integer</a>guess for the cube root,<a>i</a>.e., a number close to the cube root of 108</p>
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<p>x =<a>integer</a>guess for the cube root,<a>i</a>.e., a number close to the cube root of 108</p>
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<p><strong>Steps to find the cube root:</strong></p>
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<p><strong>Steps to find the cube root:</strong></p>
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<p>a = 108, for approximation choose, x = 4, it is the nearest cube (43=64).</p>
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<p>a = 108, for approximation choose, x = 4, it is the nearest cube (43=64).</p>
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<p> Now apply the formula; </p>
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<p> Now apply the formula; </p>
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<p>∛a≅ x((x3+2a) / (2x3+a))</p>
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<p>∛a≅ x((x3+2a) / (2x3+a))</p>
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<p>∛108≅ 4((43+2.108) / (2.43+108)) = 4.76 </p>
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<p>∛108≅ 4((43+2.108) / (2.43+108)) = 4.76 </p>
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<p>The approximate cube of 108 = 4.76 </p>
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<p>The approximate cube of 108 = 4.76 </p>
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<h2>Common mistakes and how to avoid them in cube root of 108</h2>
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<h2>Common mistakes and how to avoid them in cube root of 108</h2>
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<p>While solving ∛108, few mistakes are common in children’s worksheet. To avoid those mistakes, few solutions are given below - </p>
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<p>While solving ∛108, few mistakes are common in children’s worksheet. To avoid those mistakes, few solutions are given below - </p>
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<h3>Explore Our Programs</h3>
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<h3>Explore Our Programs</h3>
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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>(∛108+∛108)×∛108, simplify.</p>
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<p>(∛108+∛108)×∛108, simplify.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>(∛108+∛108)×∛108</p>
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<p>(∛108+∛108)×∛108</p>
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<p>= (4.762+4.762)×4.762</p>
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<p>= (4.762+4.762)×4.762</p>
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<p>= 9.524×4.762</p>
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<p>= 9.524×4.762</p>
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<p>= 45.37 </p>
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<p>= 45.37 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The simplified value is 45.37. </p>
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<p>The simplified value is 45.37. </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>If x= ∛108, find x²-x.</p>
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<p>If x= ∛108, find x²-x.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>x = 4.762</p>
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<p>x = 4.762</p>
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<p>x2 = 22.68</p>
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<p>x2 = 22.68</p>
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<p>x2 -x = 22.68-4.762</p>
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<p>x2 -x = 22.68-4.762</p>
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<p>= 17.92 </p>
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<p>= 17.92 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> x2-x is 17.92. </p>
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<p> x2-x is 17.92. </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>Multiply ∛108 and ∛216</p>
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<p>Multiply ∛108 and ∛216</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>∛108×∛216</p>
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<p>∛108×∛216</p>
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<p>= 4.762×6</p>
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<p>= 4.762×6</p>
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<p>= 28.57 </p>
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<p>= 28.57 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>multiplying value of cube root of 108 and 216 togather.</p>
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<p>multiplying value of cube root of 108 and 216 togather.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on the cube root of 108</h2>
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<h2>FAQs on the cube root of 108</h2>
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<h3>1.What is the cube of 108?</h3>
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<h3>1.What is the cube of 108?</h3>
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<h3>2.Simplify root 108.</h3>
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<h3>2.Simplify root 108.</h3>
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<h3>3.Is 108 a perfect square?</h3>
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<h3>3.Is 108 a perfect square?</h3>
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<h3>4.What are the factors of 108?</h3>
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<h3>4.What are the factors of 108?</h3>
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<p>1,2,3,4,6,9,12,18,27,36,54 and 108. </p>
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<p>1,2,3,4,6,9,12,18,27,36,54 and 108. </p>
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<h3>5.How do you make 108 a perfect cube ?</h3>
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<h3>5.How do you make 108 a perfect cube ?</h3>
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<p>You can make 108 a perfect cube by just adding 17. 108+17 =125, 125 is a perfect cube. </p>
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<p>You can make 108 a perfect cube by just adding 17. 108+17 =125, 125 is a perfect cube. </p>
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<h2>Important Glossaries for Cube root of 108</h2>
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<h2>Important Glossaries for Cube root of 108</h2>
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<ul><li><strong>Integers</strong>- Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.</li>
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<ul><li><strong>Integers</strong>- Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.</li>
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</ul><ul><li><strong>Whole numbers</strong>- The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. </li>
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</ul><ul><li><strong>Whole numbers</strong>- The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. </li>
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</ul><ul><li><strong>Square root</strong> - The square root of a number is a value “y” such that when “y” is multiplied by itself → y × y, the result is the original number. </li>
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</ul><ul><li><strong>Square root</strong> - The square root of a number is a value “y” such that when “y” is multiplied by itself → y × y, the result is the original number. </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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<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>