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2026-01-01
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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>A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of -512 and explain the methods used.</p>
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<p>A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of -512 and explain the methods used.</p>
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<h2>What is the Cube Root of -512?</h2>
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<h2>What is the Cube Root of -512?</h2>
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<p>We have learned the definition of the<a>cube</a>root. Now, let’s learn how it is represented using a<a>symbol</a>and<a>exponent</a>. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓. In<a>exponential form</a>, ∛(-512) is written as (-512)^(1/3). The cube root is just the opposite operation of finding the cube of a<a>number</a>. For example: Assume ‘y’ as the cube root of -512, then y^3 can be -512. Since -512 is a<a>perfect cube</a>, the cube root of -512 is exactly -8.</p>
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<p>We have learned the definition of the<a>cube</a>root. Now, let’s learn how it is represented using a<a>symbol</a>and<a>exponent</a>. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓. In<a>exponential form</a>, ∛(-512) is written as (-512)^(1/3). The cube root is just the opposite operation of finding the cube of a<a>number</a>. For example: Assume ‘y’ as the cube root of -512, then y^3 can be -512. Since -512 is a<a>perfect cube</a>, the cube root of -512 is exactly -8.</p>
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<h2>Finding the Cube Root of -512</h2>
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<h2>Finding the Cube Root of -512</h2>
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<p>Finding the<a>cube root</a>of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of -512. The common methods we follow to find the cube root are given below: - Prime factorization method - Approximation method - Subtraction method - Halley’s method Since -512 is a perfect cube, we can use the<a>prime factorization</a>method to find its cube root.</p>
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<p>Finding the<a>cube root</a>of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of -512. The common methods we follow to find the cube root are given below: - Prime factorization method - Approximation method - Subtraction method - Halley’s method Since -512 is a perfect cube, we can use the<a>prime factorization</a>method to find its cube root.</p>
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<h2>Cube Root of -512 by Prime Factorization</h2>
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<h2>Cube Root of -512 by Prime Factorization</h2>
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<p>Let's find the cube root of -512 using the prime factorization method. First, find the prime<a>factors</a>of -512: -512 = -1 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 Grouping the prime factors in triples, we have (-1) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = (-1) × 2^3 × 2^3 × 2^3 Thus, ∛(-512) = -2 × 2 = -8 The cube root of -512 is -8.</p>
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<p>Let's find the cube root of -512 using the prime factorization method. First, find the prime<a>factors</a>of -512: -512 = -1 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 Grouping the prime factors in triples, we have (-1) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) = (-1) × 2^3 × 2^3 × 2^3 Thus, ∛(-512) = -2 × 2 = -8 The cube root of -512 is -8.</p>
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<h2>Common Mistakes and How to Avoid Them in the Cube Root of -512</h2>
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<h2>Common Mistakes and How to Avoid Them in the Cube Root of -512</h2>
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<p>Finding the perfect cube of a number without any errors can be a difficult task for the students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:</p>
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<p>Finding the perfect cube of a number without any errors can be a difficult task for the students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Imagine you have a cube-shaped toy that has a total volume of -512 cubic centimeters. Find the length of one side of the cube equal to its cube root.</p>
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<p>Imagine you have a cube-shaped toy that has a total volume of -512 cubic centimeters. Find the length of one side of the cube equal to its cube root.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Side of the cube = ∛(-512) = -8 units</p>
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<p>Side of the cube = ∛(-512) = -8 units</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the side of the cube, we need to find the cube root of the given volume. Therefore, the side length of the cube is -8 units.</p>
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<p>To find the side of the cube, we need to find the cube root of the given volume. Therefore, the side length of the cube is -8 units.</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>A company uses -512 cubic meters of material. Calculate the amount of material left after using 100 cubic meters.</p>
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<p>A company uses -512 cubic meters of material. Calculate the amount of material left after using 100 cubic meters.</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 amount of material left is -612 cubic meters.</p>
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<p>The amount of material left is -612 cubic meters.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the remaining material, we need to account for additional usage: -512 - 100 = -612 cubic meters.</p>
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<p>To find the remaining material, we need to account for additional usage: -512 - 100 = -612 cubic meters.</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>A bottle holds -512 cubic meters of volume. Another bottle holds a volume of 100 cubic meters. What would be the total volume if the bottles are combined?</p>
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<p>A bottle holds -512 cubic meters of volume. Another bottle holds a volume of 100 cubic meters. What would be the total volume if the bottles are combined?</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 total volume of the combined bottles is -412 cubic meters.</p>
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<p>The total volume of the combined bottles is -412 cubic meters.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Explanation: Let’s add the volume of both bottles: -512 + 100 = -412 cubic meters.</p>
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<p>Explanation: Let’s add the volume of both bottles: -512 + 100 = -412 cubic meters.</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>When the cube root of -512 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?</p>
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<p>When the cube root of -512 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>2 × (-8) = -16 The cube of -16 = -4096</p>
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<p>2 × (-8) = -16 The cube of -16 = -4096</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>When we multiply the cube root of -512 by 2, it results in a larger negative volume because the cube increases exponentially.</p>
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<p>When we multiply the cube root of -512 by 2, it results in a larger negative volume because the cube increases exponentially.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Find ∛(-256 - 256).</p>
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<p>Find ∛(-256 - 256).</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>∛(-256 - 256) = ∛(-512) = -8</p>
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<p>∛(-256 - 256) = ∛(-512) = -8</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>As shown in the question ∛(-256 - 256), we combine the numbers first: -256 - 256 = -512. Then we use this step: ∛(-512) = -8 to get the answer.</p>
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<p>As shown in the question ∛(-256 - 256), we combine the numbers first: -256 - 256 = -512. Then we use this step: ∛(-512) = -8 to get the answer.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Cube Root of -512</h2>
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<h2>FAQs on Cube Root of -512</h2>
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<h3>1.Can we find the Cube Root of -512?</h3>
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<h3>1.Can we find the Cube Root of -512?</h3>
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<p>Yes, we can find the cube root of -512 exactly as the cube root of -512 is -8, a whole number.</p>
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<p>Yes, we can find the cube root of -512 exactly as the cube root of -512 is -8, a whole number.</p>
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<h3>2.Why is Cube Root of -512 rational?</h3>
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<h3>2.Why is Cube Root of -512 rational?</h3>
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<p>The cube root of -512 is rational because it is a whole number, -8, and does not have a non-repeating<a>decimal</a><a>sequence</a>.</p>
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<p>The cube root of -512 is rational because it is a whole number, -8, and does not have a non-repeating<a>decimal</a><a>sequence</a>.</p>
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<h3>3.Is it possible to get the cube root of -512 as an exact number?</h3>
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<h3>3.Is it possible to get the cube root of -512 as an exact number?</h3>
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<p>Yes, the cube root of -512 is an exact number, -8.</p>
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<p>Yes, the cube root of -512 is an exact number, -8.</p>
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<h3>4.Can we find the cube root of any number using prime factorization?</h3>
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<h3>4.Can we find the cube root of any number using prime factorization?</h3>
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<p>The prime factorization method can be used to calculate the cube root of perfect cube numbers like -512, but it is not the right method for non-perfect cube numbers.</p>
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<p>The prime factorization method can be used to calculate the cube root of perfect cube numbers like -512, but it is not the right method for non-perfect cube numbers.</p>
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<h3>5.Is there any formula to find the cube root of a number?</h3>
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<h3>5.Is there any formula to find the cube root of a number?</h3>
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<p>Yes, the<a>formula</a>we use for the cube root of any number ‘a’ is a^(1/3).</p>
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<p>Yes, the<a>formula</a>we use for the cube root of any number ‘a’ is a^(1/3).</p>
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<h2>Important Glossaries for Cube Root of -512</h2>
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<h2>Important Glossaries for Cube Root of -512</h2>
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<p>Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number. Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example: 2 × 2 × 2 = 8, therefore, 8 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a^(1/3), ⅓ is the exponent which denotes the cube root of a. Radical sign: The symbol that is used to represent a root, expressed as (∛). Rational number: A number that can be expressed as a fraction or a whole number. For example, the cube root of -512 is rational because it equals -8, which is a whole number.</p>
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<p>Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number. Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example: 2 × 2 × 2 = 8, therefore, 8 is a perfect cube. Exponent: The exponent form of the number denotes the number of times a number can be multiplied by itself. In a^(1/3), ⅓ is the exponent which denotes the cube root of a. Radical sign: The symbol that is used to represent a root, expressed as (∛). Rational number: A number that can be expressed as a fraction or a whole number. For example, the cube root of -512 is rational because it equals -8, which is a whole number.</p>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</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>