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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>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 like vehicle design, finance, etc. Here, we will discuss the square root of 81/16.</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 like vehicle design, finance, etc. Here, we will discuss the square root of 81/16.</p>
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<h2>What is the Square Root of 81/16?</h2>
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<h2>What is the Square Root of 81/16?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 81/16 is a<a>perfect square</a>. The square root of 81/16 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √(81/16), whereas (81/16)^(1/2) in the exponential form. √(81/16) = 9/4, 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<a>of</a>the square of the<a>number</a>. 81/16 is a<a>perfect square</a>. The square root of 81/16 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √(81/16), whereas (81/16)^(1/2) in the exponential form. √(81/16) = 9/4, 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 81/16</h2>
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<h2>Finding the Square Root of 81/16</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. Since 81/16 is a perfect square, we can use the prime factorization method. Let us now learn the following methods:</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. Since 81/16 is a perfect square, we can use the prime factorization method. Let us now learn the following methods:</p>
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<ul><li>Prime factorization method</li>
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<ul><li>Prime factorization method</li>
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<li>Simplification method</li>
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<li>Simplification method</li>
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</ul><h2>Square Root of 81/16 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 81/16 by Prime Factorization Method</h2>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 81 and 16 are broken down into their prime factors.</p>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. Now let us look at how 81 and 16 are broken down into their prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 81 and 16.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 81 and 16.</p>
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<p>81 is 3 × 3 × 3 × 3 (or<a>3^4</a>) 16 is 2 × 2 × 2 × 2 (or 2^4)</p>
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<p>81 is 3 × 3 × 3 × 3 (or<a>3^4</a>) 16 is 2 × 2 × 2 × 2 (or 2^4)</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 81 and 16. Since both are perfect squares, the<a>square root</a>of 81 is 3^2 = 9, and the square root of 16 is 2^2 = 4.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors of 81 and 16. Since both are perfect squares, the<a>square root</a>of 81 is 3^2 = 9, and the square root of 16 is 2^2 = 4.</p>
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<p>Therefore, √(81/16) = 9/4.</p>
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<p>Therefore, √(81/16) = 9/4.</p>
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<h2>Square Root of 81/16 by Simplification Method</h2>
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<h2>Square Root of 81/16 by Simplification Method</h2>
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<p>The simplification method is another method for finding the square roots, it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 81/16 using the simplification method.</p>
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<p>The simplification method is another method for finding the square roots, it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 81/16 using the simplification method.</p>
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<p><strong>Step 1:</strong>Simplify the<a>numerator</a>and the<a>denominator</a>separately. The numerator is 81, and the denominator is 16. The square roots of 81 and 16 are 9 and 4, respectively.</p>
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<p><strong>Step 1:</strong>Simplify the<a>numerator</a>and the<a>denominator</a>separately. The numerator is 81, and the denominator is 16. The square roots of 81 and 16 are 9 and 4, respectively.</p>
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<p><strong>Step 2:</strong>Use the<a>formula</a>: √(a/b) = √a/√b.</p>
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<p><strong>Step 2:</strong>Use the<a>formula</a>: √(a/b) = √a/√b.</p>
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<p>Therefore, √(81/16) = √81/√16 = 9/4.</p>
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<p>Therefore, √(81/16) = √81/√16 = 9/4.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 81/16</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 81/16</h2>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root. Skipping simplification methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.</p>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root. Skipping simplification methods, etc. Now let us look at a few of those mistakes that students tend to make 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 √(81/16)?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √(81/16)?</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 5.0625 square units.</p>
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<p>The area of the square is 5.0625 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 the square = side^2.</p>
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<p>The area of the square = side^2.</p>
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<p>The side length is given as √(81/16) = 9/4.</p>
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<p>The side length is given as √(81/16) = 9/4.</p>
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<p>Area of the square = (9/4)^2 = 81/16 = 5.0625.</p>
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<p>Area of the square = (9/4)^2 = 81/16 = 5.0625.</p>
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<p>Therefore, the area of the square box is 5.0625 square units.</p>
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<p>Therefore, the area of the square box is 5.0625 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 81/16 square feet is built; if each of the sides is √(81/16), what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 81/16 square feet is built; if each of the sides is √(81/16), 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>2.53125 square feet</p>
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<p>2.53125 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 81/16 by 2 = 81/32 = 2.53125.</p>
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<p>Dividing 81/16 by 2 = 81/32 = 2.53125.</p>
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<p>So half of the building measures 2.53125 square feet.</p>
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<p>So half of the building measures 2.53125 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 √(81/16) × 5.</p>
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<p>Calculate √(81/16) × 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>11.25</p>
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<p>11.25</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 81/16 which is 9/4.</p>
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<p>The first step is to find the square root of 81/16 which is 9/4.</p>
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<p>The second step is to multiply 9/4 with 5.</p>
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<p>The second step is to multiply 9/4 with 5.</p>
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<p>So (9/4) × 5 = 45/4 = 11.25.</p>
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<p>So (9/4) × 5 = 45/4 = 11.25.</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 (81 + 16)?</p>
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<p>What will be the square root of (81 + 16)?</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 9.89</p>
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<p>The square root is 9.89</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 (81 + 16). 81 + 16 = 97, and then √97 ≈ 9.849.</p>
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<p>To find the square root, we need to find the sum of (81 + 16). 81 + 16 = 97, and then √97 ≈ 9.849.</p>
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<p>Therefore, the square root of (81 + 16) is approximately ±9.89.</p>
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<p>Therefore, the square root of (81 + 16) is approximately ±9.89.</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 the rectangle if its length ‘l’ is √(81/16) units and the width ‘w’ is 38 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √(81/16) units and the width ‘w’ is 38 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>We find the perimeter of the rectangle as 96.5 units.</p>
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<p>We find the perimeter of the rectangle as 96.5 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 × (9/4 + 38) = 2 × (2.25 + 38) = 2 × 40.25 = 80.5 units.</p>
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<p>Perimeter = 2 × (9/4 + 38) = 2 × (2.25 + 38) = 2 × 40.25 = 80.5 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 81/16</h2>
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<h2>FAQ on Square Root of 81/16</h2>
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<h3>1.What is √(81/16) in its simplest form?</h3>
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<h3>1.What is √(81/16) in its simplest form?</h3>
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<p>The prime factorization of 81 is 3 × 3 × 3 × 3, and 16 is 2 × 2 × 2 × 2, so the simplest form of √(81/16) = 9/4.</p>
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<p>The prime factorization of 81 is 3 × 3 × 3 × 3, and 16 is 2 × 2 × 2 × 2, so the simplest form of √(81/16) = 9/4.</p>
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<h3>2.Mention the factors of 81 and 16.</h3>
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<h3>2.Mention the factors of 81 and 16.</h3>
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<p>Factors of 81 are 1, 3, 9, 27, and 81. Factors of 16 are 1, 2, 4, 8, and 16.</p>
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<p>Factors of 81 are 1, 3, 9, 27, and 81. Factors of 16 are 1, 2, 4, 8, and 16.</p>
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<h3>3.Calculate the square of 81/16.</h3>
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<h3>3.Calculate the square of 81/16.</h3>
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<p>We get the square of 81/16 by multiplying the number by itself, that is (81/16) × (81/16) = 6561/256.</p>
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<p>We get the square of 81/16 by multiplying the number by itself, that is (81/16) × (81/16) = 6561/256.</p>
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<h3>4.Is 81/16 a rational number?</h3>
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<h3>4.Is 81/16 a rational number?</h3>
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<p>Yes, 81/16 is a rational number, as it can be expressed as a<a>fraction</a>where both the numerator and the denominator are integers.</p>
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<p>Yes, 81/16 is a rational number, as it can be expressed as a<a>fraction</a>where both the numerator and the denominator are integers.</p>
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<h3>5.81/16 is divisible by?</h3>
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<h3>5.81/16 is divisible by?</h3>
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<p>81/16 is a fraction, and its divisibility depends on the context. However, the numerator 81 is divisible by 1, 3, 9, 27, and 81, and the denominator 16 is divisible by 1, 2, 4, 8, and 16.</p>
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<p>81/16 is a fraction, and its divisibility depends on the context. However, the numerator 81 is divisible by 1, 3, 9, 27, and 81, and the denominator 16 is divisible by 1, 2, 4, 8, and 16.</p>
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<h2>Important Glossaries for the Square Root of 81/16</h2>
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<h2>Important Glossaries for the Square Root of 81/16</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse of a square. Example: 4^2 = 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: 4^2 = 16, and the inverse of the square is the square root, that is, √16 = 4.</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 q is not equal to zero, and p and q are integers.</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 q is not equal to zero, and p and q are integers.</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. For example, 16 is a perfect square because 4 × 4 = 16.</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. For example, 16 is a perfect square because 4 × 4 = 16.</li>
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</ul><ul><li><strong>Fraction:</strong>A fraction is a numerical quantity that is not a whole number, represented by two numbers separated by a slash, such as 3/4.</li>
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</ul><ul><li><strong>Fraction:</strong>A fraction is a numerical quantity that is not a whole number, represented by two numbers separated by a slash, such as 3/4.</li>
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</ul><ul><li><strong>Simplification:</strong>Simplification is the process of reducing a mathematical expression to its simplest form.</li>
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</ul><ul><li><strong>Simplification:</strong>Simplification is the process of reducing a mathematical expression to its simplest form.</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>