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2026-01-01
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2026-02-28
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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>If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. Square roots are used in various fields like physics, engineering, and computer graphics. Here, we will discuss the square root of -63.</p>
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<p>If a number is multiplied by itself, the result is a square. The inverse of the square is a square root. Square roots are used in various fields like physics, engineering, and computer graphics. Here, we will discuss the square root of -63.</p>
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<h2>What is the Square Root of -63?</h2>
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<h2>What is the Square Root of -63?</h2>
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<p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. Since -63 is negative, it does not have a real square root. In mathematics, the square root of a<a>negative number</a>is expressed using the imaginary unit 'i', where i² = -1. Therefore, the square root of -63 is expressed as √-63 = √63 * i or approximately 7.937 * i, which is a<a>complex number</a>.</p>
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<p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. Since -63 is negative, it does not have a real square root. In mathematics, the square root of a<a>negative number</a>is expressed using the imaginary unit 'i', where i² = -1. Therefore, the square root of -63 is expressed as √-63 = √63 * i or approximately 7.937 * i, which is a<a>complex number</a>.</p>
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<h2>Understanding Imaginary Numbers</h2>
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<h2>Understanding Imaginary Numbers</h2>
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<p>The concept of imaginary numbers is used to denote the square roots of negative numbers. The imaginary unit 'i' is defined such that i² = -1. Therefore, the square root of -63 can be written as: √-63 = √63 * i The value √63 is approximately 7.937.</p>
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<p>The concept of imaginary numbers is used to denote the square roots of negative numbers. The imaginary unit 'i' is defined such that i² = -1. Therefore, the square root of -63 can be written as: √-63 = √63 * i The value √63 is approximately 7.937.</p>
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<p>Thus, the square root of -63 is written as 7.937 * i.</p>
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<p>Thus, the square root of -63 is written as 7.937 * i.</p>
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<h2>Expressing Complex Numbers</h2>
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<h2>Expressing Complex Numbers</h2>
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<p>Complex numbers consist of a real part and an imaginary part. Here, since we are finding the square root of a negative number, the result is purely imaginary with no real component.</p>
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<p>Complex numbers consist of a real part and an imaginary part. Here, since we are finding the square root of a negative number, the result is purely imaginary with no real component.</p>
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<p>Thus, the square root of -63 is a complex number expressed as: √-63 = 0 + 7.937 * i</p>
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<p>Thus, the square root of -63 is a complex number expressed as: √-63 = 0 + 7.937 * i</p>
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<h2>Applications of Imaginary Numbers</h2>
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<h2>Applications of Imaginary Numbers</h2>
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<p>Imaginary numbers, though not real, have practical applications in various fields. They are used in electrical engineering to describe the behavior of currents and voltages, in signal processing, and in<a>solving equations</a>that describe wave behaviors. Understanding and expressing square roots of negative numbers is vital in these fields.</p>
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<p>Imaginary numbers, though not real, have practical applications in various fields. They are used in electrical engineering to describe the behavior of currents and voltages, in signal processing, and in<a>solving equations</a>that describe wave behaviors. Understanding and expressing square roots of negative numbers is vital in these fields.</p>
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<h2>Common Mistakes and How to Avoid Them with Square Roots of Negative Numbers</h2>
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<h2>Common Mistakes and How to Avoid Them with Square Roots of Negative Numbers</h2>
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<p>Students may struggle with square roots of negative numbers, often neglecting the imaginary component. Let's examine common mistakes and how to address them.</p>
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<p>Students may struggle with square roots of negative numbers, often neglecting the imaginary component. Let's examine common mistakes and how to address them.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you find the square root of -49?</p>
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<p>Can you find the square root of -49?</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 is 7i.</p>
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<p>The square root is 7i.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Since -49 is negative, its square root involves 'i'.</p>
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<p>Since -49 is negative, its square root involves 'i'.</p>
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<p>The square root of 49 is 7, so the square root of -49 is 7i.</p>
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<p>The square root of 49 is 7, so the square root of -49 is 7i.</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>What is the square of the imaginary unit 'i'?</p>
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<p>What is the square of the imaginary unit 'i'?</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 is -1.</p>
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<p>The square is -1.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>By definition, i² = -1.</p>
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<p>By definition, i² = -1.</p>
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<p>This is a fundamental property of the imaginary unit.</p>
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<p>This is a fundamental property of the imaginary unit.</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>Calculate 3 times the square root of -9.</p>
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<p>Calculate 3 times the square root of -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>The result is 9i.</p>
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<p>The result is 9i.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The square root of -9 is 3i.</p>
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<p>The square root of -9 is 3i.</p>
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<p>Multiplying by 3 gives 9i.</p>
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<p>Multiplying by 3 gives 9i.</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>What is the sum of the square roots of -16 and -25?</p>
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<p>What is the sum of the square roots of -16 and -25?</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 is 7i.</p>
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<p>The sum is 7i.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The square root of -16 is 4i, and the square root of -25 is 5i.</p>
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<p>The square root of -16 is 4i, and the square root of -25 is 5i.</p>
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<p>Adding these gives 9i.</p>
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<p>Adding these gives 9i.</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 the square root of -81.</p>
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<p>Find the square root of -81.</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 is 9i.</p>
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<p>The square root is 9i.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The square root of 81 is 9, so the square root of -81 is 9i.</p>
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<p>The square root of 81 is 9, so the square root of -81 is 9i.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQ on Square Root of -63</h2>
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<h2>FAQ on Square Root of -63</h2>
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<h3>1.What is √-63 in its simplest form?</h3>
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<h3>1.What is √-63 in its simplest form?</h3>
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<p>The simplest form of √-63 is √63 * i, where i is the imaginary unit.</p>
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<p>The simplest form of √-63 is √63 * i, where i is the imaginary unit.</p>
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<h3>2.Can negative numbers have real square roots?</h3>
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<h3>2.Can negative numbers have real square roots?</h3>
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<p>No, negative numbers do not have real square roots. Their square roots are imaginary numbers.</p>
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<p>No, negative numbers do not have real square roots. Their square roots are imaginary numbers.</p>
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<h3>3.What does the imaginary unit 'i' represent?</h3>
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<h3>3.What does the imaginary unit 'i' represent?</h3>
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<p>The imaginary unit 'i' is defined such that i² = -1. It is used to represent square roots of negative numbers.</p>
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<p>The imaginary unit 'i' is defined such that i² = -1. It is used to represent square roots of negative numbers.</p>
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<h3>4.Are there any real applications of imaginary numbers?</h3>
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<h3>4.Are there any real applications of imaginary numbers?</h3>
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<p>Yes, imaginary numbers are used in electrical engineering, control systems, signal processing, and quantum physics, among other fields.</p>
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<p>Yes, imaginary numbers are used in electrical engineering, control systems, signal processing, and quantum physics, among other fields.</p>
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<h3>5.How can I express the square root of -100?</h3>
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<h3>5.How can I express the square root of -100?</h3>
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<p>The square root of -100 is 10i, as the square root of 100 is 10.</p>
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<p>The square root of -100 is 10i, as the square root of 100 is 10.</p>
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<h2>Important Glossaries for the Square Root of -63</h2>
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<h2>Important Glossaries for the Square Root of -63</h2>
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<ul><li><strong>Imaginary unit:</strong>The imaginary unit 'i' is defined as √-1. It is used to express the square roots of negative numbers. </li>
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<ul><li><strong>Imaginary unit:</strong>The imaginary unit 'i' is defined as √-1. It is used to express the square roots of negative numbers. </li>
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<li><strong>Complex number:</strong>A complex number has a real part and an imaginary part, typically written as a + bi. </li>
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<li><strong>Complex number:</strong>A complex number has a real part and an imaginary part, typically written as a + bi. </li>
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<li><strong>Imaginary number:</strong>A number that can be written as a real number multiplied by the imaginary unit 'i'. For example, 3i is an imaginary number. </li>
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<li><strong>Imaginary number:</strong>A number that can be written as a real number multiplied by the imaginary unit 'i'. For example, 3i is an imaginary number. </li>
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<li><strong>Complex plane:</strong>A plane used to represent complex numbers graphically, with the horizontal axis representing the real part and the vertical axis representing the imaginary part. </li>
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<li><strong>Complex plane:</strong>A plane used to represent complex numbers graphically, with the horizontal axis representing the real part and the vertical axis representing the imaginary part. </li>
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<li><strong>Square root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. For negative numbers, the result involves imaginary numbers.</li>
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<li><strong>Square root:</strong>The square root of a number is a value that, when multiplied by itself, gives the original number. For negative numbers, the result involves imaginary numbers.</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>