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2026-01-01
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2026-02-28
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<p>452 Learners</p>
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<p>507 Learners</p>
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<p>Last updated on<strong>October 23, 2025</strong></p>
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<p>Last updated on<strong>October 23, 2025</strong></p>
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<p>When someone asks you to explain a square root, you can just tell that it is a number when multiplied by itself produces the same number. As we continue with our explanation, let’s assume the value of 83 Here 83 is considered as a non-perfect square root since it contain either decimal or fraction. Let's learn more about square roots in this article.</p>
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<p>When someone asks you to explain a square root, you can just tell that it is a number when multiplied by itself produces the same number. As we continue with our explanation, let’s assume the value of 83 Here 83 is considered as a non-perfect square root since it contain either decimal or fraction. Let's learn more about square roots in this article.</p>
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<h2>What is the square root of 83?</h2>
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<h2>What is the square root of 83?</h2>
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<p>The<a>square</a>root of 83 can be easily found out by using<a>long division</a>method. In which it is discovered that the cumulative approximation of √83 is 9.110. </p>
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<p>The<a>square</a>root of 83 can be easily found out by using<a>long division</a>method. In which it is discovered that the cumulative approximation of √83 is 9.110. </p>
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<h2>Finding the square root of 83.</h2>
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<h2>Finding the square root of 83.</h2>
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<p>There are many ways through which students can find square roots, and some of these methods are very popular. Some of the methods have been explained in detail below. </p>
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<p>There are many ways through which students can find square roots, and some of these methods are very popular. Some of the methods have been explained in detail below. </p>
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<h3>Square root of 83 using the prime factorization method.</h3>
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<h3>Square root of 83 using the prime factorization method.</h3>
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<p>In this method, we decompose the<a>number</a>into its<a>prime factors</a>.</p>
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<p>In this method, we decompose the<a>number</a>into its<a>prime factors</a>.</p>
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<p>Prime factorization of 83: 83 = 1×83</p>
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<p>Prime factorization of 83: 83 = 1×83</p>
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<p>Since not all prime factors can be paired, 83 cannot be simplified into a<a>perfect square</a>. Therefore, the<a>square root</a>of 83 cannot be expressed in a simple radical form.</p>
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<p>Since not all prime factors can be paired, 83 cannot be simplified into a<a>perfect square</a>. Therefore, the<a>square root</a>of 83 cannot be expressed in a simple radical form.</p>
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<h3>Square root of 83 using the division method.</h3>
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<h3>Square root of 83 using the division method.</h3>
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<p>For non-perfect squares, we often use the nearest perfect square to estimate the square root. Follow these steps:</p>
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<p>For non-perfect squares, we often use the nearest perfect square to estimate the square root. Follow these steps:</p>
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<p><strong>Step 1:</strong>Write the number 83 to perform long<a>division</a>.</p>
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<p><strong>Step 1:</strong>Write the number 83 to perform long<a>division</a>.</p>
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<p><strong>Step 2:</strong>Identify a perfect square number that is<a>less than</a>or equal to 83. For 83, that number is 64 (8²).</p>
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<p><strong>Step 2:</strong>Identify a perfect square number that is<a>less than</a>or equal to 83. For 83, that number is 64 (8²).</p>
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<p><strong>Step 3:</strong>Divide 83 by 8. The<a>remainder</a>will be 19, and the<a>quotient</a>will be 10.</p>
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<p><strong>Step 3:</strong>Divide 83 by 8. The<a>remainder</a>will be 19, and the<a>quotient</a>will be 10.</p>
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<p><strong>Step 4:</strong>Bring down the remainder (19) and append two zeros. Add a<a>decimal</a>point to the quotient, making it 10.0.</p>
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<p><strong>Step 4:</strong>Bring down the remainder (19) and append two zeros. Add a<a>decimal</a>point to the quotient, making it 10.0.</p>
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<p><strong>Step 5:</strong>Double the quotient to use as the new<a>divisor</a>, which gives 20.</p>
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<p><strong>Step 5:</strong>Double the quotient to use as the new<a>divisor</a>, which gives 20.</p>
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<p><strong>Step 6:</strong>Select a number that, when multiplied by the new divisor, results in a<a>product</a>less than or equal to 1900.</p>
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<p><strong>Step 6:</strong>Select a number that, when multiplied by the new divisor, results in a<a>product</a>less than or equal to 1900.</p>
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<p><strong>Step 7:</strong>Continue the division process to find √83 to the desired decimal places. → √83 ≈ 9.110.</p>
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<p><strong>Step 7:</strong>Continue the division process to find √83 to the desired decimal places. → √83 ≈ 9.110.</p>
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<h3>Square root of 83 using the approximation method</h3>
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<h3>Square root of 83 using the approximation method</h3>
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<p>In the approximation method, we estimate the square root by identifying the closest perfect squares surrounding the number.</p>
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<p>In the approximation method, we estimate the square root by identifying the closest perfect squares surrounding the number.</p>
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<p><strong>Step 1:</strong>The nearest perfect squares to 83 are √100 = 10 and √81 = 9.</p>
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<p><strong>Step 1:</strong>The nearest perfect squares to 83 are √100 = 10 and √81 = 9.</p>
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<p><strong>Step 2:</strong>Since 83 is between 100 and 81, we know the square root will be between 10 and 9.</p>
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<p><strong>Step 2:</strong>Since 83 is between 100 and 81, we know the square root will be between 10 and 9.</p>
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<p><strong>Step 3:</strong>By testing numbers like 9.1, 9.2 and further, we find that √83 ≈ 9.110. </p>
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<p><strong>Step 3:</strong>By testing numbers like 9.1, 9.2 and further, we find that √83 ≈ 9.110. </p>
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<h2>Common mistakes when finding the square root of 83.</h2>
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<h2>Common mistakes when finding the square root of 83.</h2>
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<p>Here are some common mistakes students should avoid while learning to calculate the square root of 83. </p>
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<p>Here are some common mistakes students should avoid while learning to calculate the square root of 83. </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>What is the square root of 0?</p>
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<p>What is the square root of 0?</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 square root of 0 is 0. </p>
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<p>→The square root of 0 is 0. </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Since 0×0=0 the square root of 0 is 0. </p>
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<p>Since 0×0=0 the square root of 0 is 0. </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>Is √81 greater than 9.</p>
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<p>Is √81 greater than 9.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>√81 = 9 </p>
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<p>√81 = 9 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> Since 81 is a perfect square, √81 = 9, which is equal to 9 not greater than 9. </p>
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<p> Since 81 is a perfect square, √81 = 9, which is equal to 9 not greater than 9. </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>How do you find the square root of a non-perfect square, such as √18?</p>
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<p>How do you find the square root of a non-perfect square, such as √18?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>→ √18</p>
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<p>→ √18</p>
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<p>√18 = 3√2 </p>
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<p>√18 = 3√2 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>18 can be factored as 9×2 and 9 can be further factorized to 3 hence the final answer would be 3√2. </p>
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<p>18 can be factored as 9×2 and 9 can be further factorized to 3 hence the final answer would be 3√2. </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 square root of 83</h2>
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<h2>FAQs on the square root of 83</h2>
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<h3>1. Is 83 a prime number?</h3>
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<h3>1. Is 83 a prime number?</h3>
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<p>Yes, If we use long division on 83 we get to know that it has only two divisors which are 1 and itself, so it is a<a>prime number</a>. </p>
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<p>Yes, If we use long division on 83 we get to know that it has only two divisors which are 1 and itself, so it is a<a>prime number</a>. </p>
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<h3>2. How do you simplify 8√80?</h3>
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<h3>2. How do you simplify 8√80?</h3>
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<p> 8√80 can be simplified to 32√5, as we can express √80 as 4√5. 8 × 4 is equal to 32 hence it will be written as 32√5. </p>
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<p> 8√80 can be simplified to 32√5, as we can express √80 as 4√5. 8 × 4 is equal to 32 hence it will be written as 32√5. </p>
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<h3>3.What is the difference between square root and cube root?</h3>
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<h3>3.What is the difference between square root and cube root?</h3>
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<p> A square root of a number is a value that, when multiplied by itself, gives that number. The<a>cube root</a>is a value that, when multiplied by itself twice, then the result is the said number. </p>
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<p> A square root of a number is a value that, when multiplied by itself, gives that number. The<a>cube root</a>is a value that, when multiplied by itself twice, then the result is the said number. </p>
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<h3>4.What is the square root of 49?</h3>
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<h3>4.What is the square root of 49?</h3>
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<p> By applying the long division method on 49 we get to know that 7 divides 49 to 0 using 7 meaning 7 × 7 is equal to 49, which makes 7 the square root of 49. </p>
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<p> By applying the long division method on 49 we get to know that 7 divides 49 to 0 using 7 meaning 7 × 7 is equal to 49, which makes 7 the square root of 49. </p>
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<h3>5.What is the prime factorization of 83?</h3>
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<h3>5.What is the prime factorization of 83?</h3>
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<p>Using the prime factorization method, we can easily find out that 83 can be written as<a>multiples</a>of 1 and 83 to be more specific 83=1×83. Since it is a prime number. </p>
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<p>Using the prime factorization method, we can easily find out that 83 can be written as<a>multiples</a>of 1 and 83 to be more specific 83=1×83. Since it is a prime number. </p>
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<ul><li><strong>Square Root:</strong>A number which when is multiplied by itself gives the original number is called a square root.</li>
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<ul><li><strong>Square Root:</strong>A number which when is multiplied by itself gives the original number is called a square root.</li>
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</ul><ul><li><strong>Perfect Square:</strong>A number that is the integral square of an<a>integer</a>I such that n = I², example I = 1, 2, 3, n = 1, 4, 9, 16, etc.</li>
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</ul><ul><li><strong>Perfect Square:</strong>A number that is the integral square of an<a>integer</a>I such that n = I², example I = 1, 2, 3, n = 1, 4, 9, 16, etc.</li>
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</ul><ul><li><strong>Prime Factorization:</strong>The ability to factorize a number in to the product of the basic<a>arithmetic</a>numbers, also known as primary numbers.</li>
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</ul><ul><li><strong>Prime Factorization:</strong>The ability to factorize a number in to the product of the basic<a>arithmetic</a>numbers, also known as primary numbers.</li>
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</ul><ul><li><strong>Non-Perfect Square:</strong>A figure that cannot be converted into an integer figure once divided by itself (e.g., 76).</li>
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</ul><ul><li><strong>Non-Perfect Square:</strong>A figure that cannot be converted into an integer figure once divided by itself (e.g., 76).</li>
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</ul><ul><li><strong>Approximation Method:</strong>Approximating square root, that is, finding the closest integer which, when squared, yields the number being approximated.</li>
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</ul><ul><li><strong>Approximation Method:</strong>Approximating square root, that is, finding the closest integer which, when squared, yields the number being approximated.</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>