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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 the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1/64.</p>
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<p>If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design, finance, etc. Here, we will discuss the square root of 1/64.</p>
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<h2>What is the Square Root of 1/64?</h2>
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<h2>What is the Square Root of 1/64?</h2>
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<p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 1/64 is a<a>perfect square</a>. The square root of 1/64 can be expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √(1/64), whereas (1/64)^(1/2) is the exponential form. √(1/64) = 1/8, which is a<a>rational number</a>because it can be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<p>The<a>square</a>root is the inverse of the square of a<a>number</a>. 1/64 is a<a>perfect square</a>. The square root of 1/64 can be expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √(1/64), whereas (1/64)^(1/2) is the exponential form. √(1/64) = 1/8, which is a<a>rational number</a>because it can be expressed in the form of p/q, where p and q are<a>integers</a>and q ≠ 0.</p>
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<h2>Finding the Square Root of 1/64</h2>
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<h2>Finding the Square Root of 1/64</h2>
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<p>For perfect square numbers, the<a>prime factorization</a>method is often used. However, since 1/64 is already a perfect square, we can find its<a>square root</a>directly using the following methods:</p>
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<p>For perfect square numbers, the<a>prime factorization</a>method is often used. However, since 1/64 is already a perfect square, we can find its<a>square root</a>directly using the following methods:</p>
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<ul><li>Direct calculation </li>
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<ul><li>Direct calculation </li>
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<li>Prime factorization method</li>
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<li>Prime factorization method</li>
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</ul><h3>Square Root of 1/64 by Direct Calculation</h3>
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</ul><h3>Square Root of 1/64 by Direct Calculation</h3>
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<p>Since 1/64 is a perfect square, we can find its square root directly:</p>
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<p>Since 1/64 is a perfect square, we can find its square root directly:</p>
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<p>Step 1: Recognize that 1/64 can be rewritten as (1/8)².</p>
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<p>Step 1: Recognize that 1/64 can be rewritten as (1/8)².</p>
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<p>Step 2: The square root of (1/8)² is simply 1/8. Therefore, √(1/64) = 1/8.</p>
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<p>Step 2: The square root of (1/8)² is simply 1/8. Therefore, √(1/64) = 1/8.</p>
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<h3>Square Root of 1/64 by Prime Factorization Method</h3>
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<h3>Square Root of 1/64 by Prime Factorization Method</h3>
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<p>The prime factorization method involves expressing the number as a<a>product</a>of<a>prime numbers</a>. Since 1 is already a perfect square, we focus on 64:</p>
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<p>The prime factorization method involves expressing the number as a<a>product</a>of<a>prime numbers</a>. Since 1 is already a perfect square, we focus on 64:</p>
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<p><strong>Step 1:</strong>Find the prime<a>factors</a>of 64. Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 = 2^6.</p>
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<p><strong>Step 1:</strong>Find the prime<a>factors</a>of 64. Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 = 2^6.</p>
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<p><strong>Step 2:</strong>The prime factorization of 64 is 2^6. The square root of 64 is found by halving the<a>exponent</a>of the prime factors: √(2^6) = 2^3 = 8.</p>
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<p><strong>Step 2:</strong>The prime factorization of 64 is 2^6. The square root of 64 is found by halving the<a>exponent</a>of the prime factors: √(2^6) = 2^3 = 8.</p>
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<p><strong>Step 3:</strong>Therefore, √(1/64) = 1/√64 = 1/8.</p>
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<p><strong>Step 3:</strong>Therefore, √(1/64) = 1/√64 = 1/8.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1/64</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1/64</h2>
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<p>Students do sometimes make mistakes while finding the square root, such as forgetting about negative square roots or misapplying methods. Let's look at a few of these mistakes in detail.</p>
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<p>Students do sometimes make mistakes while finding the square root, such as forgetting about negative square roots or misapplying methods. Let's look at a few of these mistakes in detail.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1/64</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1/64</h2>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping proper simplification methods. Let's look at a few of these mistakes in detail.</p>
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<p>Students do make mistakes while finding the square root, such as forgetting about the negative square root or skipping proper simplification methods. Let's look at a few of these mistakes in detail.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Can you help Max find the area of a square box if its side length is given as √(1/64)?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √(1/64)?</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 area of the square is 1/64 square units.</p>
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<p>The area of the square is 1/64 square units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The area of a square = side².</p>
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<p>The area of a square = side².</p>
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<p>The side length is given as √(1/64).</p>
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<p>The side length is given as √(1/64).</p>
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<p>Area of the square = side² = (1/8) x (1/8) = 1/64.</p>
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<p>Area of the square = side² = (1/8) x (1/8) = 1/64.</p>
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<p>Therefore, the area of the square box is 1/64 square units.</p>
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<p>Therefore, the area of the square box is 1/64 square 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 square-shaped building measuring 1/64 square feet is built; if each of the sides is √(1/64), what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 1/64 square feet is built; if each of the sides is √(1/64), what will be the square feet of half of the building?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>1/128 square feet</p>
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<p>1/128 square feet</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can just divide the given area by 2 as the building is square-shaped.</p>
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<p>We can just divide the given area by 2 as the building is square-shaped.</p>
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<p>Dividing 1/64 by 2 = 1/128.</p>
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<p>Dividing 1/64 by 2 = 1/128.</p>
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<p>So half of the building measures 1/128 square feet.</p>
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<p>So half of the building measures 1/128 square feet.</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 √(1/64) x 5.</p>
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<p>Calculate √(1/64) x 5.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>5/8</p>
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<p>5/8</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The first step is to find the square root of 1/64, which is 1/8.</p>
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<p>The first step is to find the square root of 1/64, which is 1/8.</p>
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<p>The second step is to multiply 1/8 by 5.</p>
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<p>The second step is to multiply 1/8 by 5.</p>
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<p>So, (1/8) x 5 = 5/8.</p>
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<p>So, (1/8) x 5 = 5/8.</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 will be the square root of (1/64 + 1/64)?</p>
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<p>What will be the square root of (1/64 + 1/64)?</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 1/4.</p>
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<p>The square root is 1/4.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the square root, we need to find the sum of (1/64 + 1/64).</p>
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<p>To find the square root, we need to find the sum of (1/64 + 1/64).</p>
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<p>1/64 + 1/64 = 2/64 = 1/32, and then √(1/32) = 1/√32 ≈ 1/5.65685 = 1/4 (approximately).</p>
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<p>1/64 + 1/64 = 2/64 = 1/32, and then √(1/32) = 1/√32 ≈ 1/5.65685 = 1/4 (approximately).</p>
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<p>Therefore, the square root of (1/64 + 1/64) is approximately 1/4.</p>
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<p>Therefore, the square root of (1/64 + 1/64) is approximately 1/4.</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 perimeter of a rectangle if its length 'l' is √(1/64) units and the width 'w' is 1/4 units.</p>
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<p>Find the perimeter of a rectangle if its length 'l' is √(1/64) units and the width 'w' is 1/4 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>The perimeter of the rectangle is 3/4 units.</p>
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<p>The perimeter of the rectangle is 3/4 units.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Perimeter of the rectangle = 2 × (length + width).</p>
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<p>Perimeter of the rectangle = 2 × (length + width).</p>
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<p>Perimeter = 2 × (√(1/64) + 1/4) = 2 × (1/8 + 1/4) = 2 × (1/8 + 2/8) = 2 × (3/8) = 6/8 = 3/4 units.</p>
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<p>Perimeter = 2 × (√(1/64) + 1/4) = 2 × (1/8 + 1/4) = 2 × (1/8 + 2/8) = 2 × (3/8) = 6/8 = 3/4 units.</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 1/64</h2>
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<h2>FAQ on Square Root of 1/64</h2>
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<h3>1.What is √(1/64) in its simplest form?</h3>
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<h3>1.What is √(1/64) in its simplest form?</h3>
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<p>The simplest form of √(1/64) is 1/8 since 1/64 can be expressed as (1/8)².</p>
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<p>The simplest form of √(1/64) is 1/8 since 1/64 can be expressed as (1/8)².</p>
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<h3>2.What are the factors of 64?</h3>
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<h3>2.What are the factors of 64?</h3>
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<p>Factors of 64 are 1, 2, 4, 8, 16, 32, and 64.</p>
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<p>Factors of 64 are 1, 2, 4, 8, 16, 32, and 64.</p>
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<h3>3.Calculate the square of 1/8.</h3>
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<h3>3.Calculate the square of 1/8.</h3>
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<p>We get the square of 1/8 by multiplying the number by itself: (1/8) x (1/8) = 1/64.</p>
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<p>We get the square of 1/8 by multiplying the number by itself: (1/8) x (1/8) = 1/64.</p>
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<h3>4.Is 1/64 a perfect square?</h3>
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<h3>4.Is 1/64 a perfect square?</h3>
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<p>Yes, 1/64 is a perfect square because it can be expressed as (1/8)².</p>
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<p>Yes, 1/64 is a perfect square because it can be expressed as (1/8)².</p>
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<h3>5.Is 64 a prime number?</h3>
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<h3>5.Is 64 a prime number?</h3>
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<p>No, 64 is not a prime number, as it has more than two factors.</p>
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<p>No, 64 is not a prime number, as it has more than two factors.</p>
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<h2>Important Glossaries for the Square Root of 1/64</h2>
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<h2>Important Glossaries for the Square Root of 1/64</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that is √16 = 4.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4² = 16 and the inverse of the square is the square root, that is √16 = 4.</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. Example: 64 is a perfect square because it is 8².</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is a number that is the square of an integer. Example: 64 is a perfect square because it is 8².</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, where p and q are integers and q is not equal to zero.</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be written in the form of p/q, where p and q are integers and q is not equal to zero.</li>
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</ul><ul><li><strong>Exponent:</strong>An exponent refers to the number that indicates how many times a base is multiplied by itself. Example: In 2^3, 3 is the exponent.</li>
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</ul><ul><li><strong>Exponent:</strong>An exponent refers to the number that indicates how many times a base is multiplied by itself. Example: In 2^3, 3 is the exponent.</li>
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</ul><ul><li><strong>Fraction:</strong>A fraction represents a part of a whole and is expressed as p/q, where p and q are integers and q ≠ 0.</li>
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</ul><ul><li><strong>Fraction:</strong>A fraction represents a part of a whole and is expressed as p/q, where p and q are integers and q ≠ 0.</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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<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>