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2026-01-01
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2026-02-28
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<p>254 Learners</p>
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<p>294 Learners</p>
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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 squaring a number is finding its square root. Square roots are used in various fields such as engineering, finance, and architecture. Here, we will discuss the square root of 49/81.</p>
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<p>If a number is multiplied by itself, the result is a square. The inverse of squaring a number is finding its square root. Square roots are used in various fields such as engineering, finance, and architecture. Here, we will discuss the square root of 49/81.</p>
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<h2>What is the Square Root of 49/81?</h2>
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<h2>What is the Square Root of 49/81?</h2>
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<p>The<a>square</a>root is the inverse operation of squaring a<a>number</a>. The<a>fraction</a>49/81 is a<a>perfect square</a>. The square root of 49/81 can be expressed in both radical and<a>exponential form</a>. In radical form, it is written as √(49/81), and in exponential form, it is written as (49/81)^(1/2). The square root of 49/81 is 7/9, 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 operation of squaring a<a>number</a>. The<a>fraction</a>49/81 is a<a>perfect square</a>. The square root of 49/81 can be expressed in both radical and<a>exponential form</a>. In radical form, it is written as √(49/81), and in exponential form, it is written as (49/81)^(1/2). The square root of 49/81 is 7/9, 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 49/81</h2>
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<h2>Finding the Square Root of 49/81</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers, including fractions. Let's explore the methods to find the<a>square root</a>of a fraction:</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers, including fractions. Let's explore the methods to find the<a>square root</a>of a fraction:</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 49/81 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 49/81 by Prime Factorization Method</h2>
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<p>The prime factorization method involves expressing numbers as the<a>product</a>of their prime<a>factors</a>. Let's see how 49/81 is broken down:</p>
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<p>The prime factorization method involves expressing numbers as the<a>product</a>of their prime<a>factors</a>. Let's see how 49/81 is broken down:</p>
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<p><strong>Step 1:</strong>Prime factorization of 49 is 7 × 7, and for 81, it is 3 × 3 × 3 × 3.</p>
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<p><strong>Step 1:</strong>Prime factorization of 49 is 7 × 7, and for 81, it is 3 × 3 × 3 × 3.</p>
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<p><strong>Step 2:</strong>We can write 49/81 as (7 × 7)/(3 × 3 × 3 × 3).</p>
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<p><strong>Step 2:</strong>We can write 49/81 as (7 × 7)/(3 × 3 × 3 × 3).</p>
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<p><strong>Step 3:</strong>Taking the square root of both the<a>numerator</a>and the<a>denominator</a>separately gives us √49/√81 = 7/9. Therefore, the square root of 49/81 is 7/9.</p>
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<p><strong>Step 3:</strong>Taking the square root of both the<a>numerator</a>and the<a>denominator</a>separately gives us √49/√81 = 7/9. Therefore, the square root of 49/81 is 7/9.</p>
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<h2>Square Root of 49/81 by Simplification Method</h2>
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<h2>Square Root of 49/81 by Simplification Method</h2>
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<p>The simplification method involves simplifying the fraction before finding its square root. Let's see how we can do this:</p>
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<p>The simplification method involves simplifying the fraction before finding its square root. Let's see how we can do this:</p>
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<p><strong>Step 1:</strong>Identify the perfect squares in the<a>numerator and denominator</a>. 49 is a perfect square of 7, and 81 is a perfect square of 9.</p>
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<p><strong>Step 1:</strong>Identify the perfect squares in the<a>numerator and denominator</a>. 49 is a perfect square of 7, and 81 is a perfect square of 9.</p>
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<p><strong>Step 2:</strong>The square root of 49 is 7, and the square root of 81 is 9.</p>
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<p><strong>Step 2:</strong>The square root of 49 is 7, and the square root of 81 is 9.</p>
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<p><strong>Step 3:</strong>Thus, the square root of 49/81 is 7/9.</p>
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<p><strong>Step 3:</strong>Thus, the square root of 49/81 is 7/9.</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 √(49/81)?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √(49/81)?</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 area of the square is 49/81 square units.</p>
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<p>The area of the square is 49/81 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 = side².</p>
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<p>The area of the square = side².</p>
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<p>The side length is given as √(49/81).</p>
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<p>The side length is given as √(49/81).</p>
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<p>Area = (7/9) × (7/9) = 49/81.</p>
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<p>Area = (7/9) × (7/9) = 49/81.</p>
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<p>Therefore, the area of the square box is 49/81 square units.</p>
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<p>Therefore, the area of the square box is 49/81 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 plot measures 49/81 square meters in area; if each side is √(49/81), what will be the area of half of the plot?</p>
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<p>A square-shaped plot measures 49/81 square meters in area; if each side is √(49/81), what will be the area of half of the plot?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>49/162 square meters</p>
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<p>49/162 square meters</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The plot's area is 49/81 square meters.</p>
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<p>The plot's area is 49/81 square meters.</p>
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<p>To find half of this area, divide by 2. (49/81) ÷ 2 = 49/162.</p>
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<p>To find half of this area, divide by 2. (49/81) ÷ 2 = 49/162.</p>
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<p>So, half of the plot measures 49/162 square meters.</p>
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<p>So, half of the plot measures 49/162 square 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>Calculate √(49/81) × 5.</p>
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<p>Calculate √(49/81) × 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>35/9</p>
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<p>35/9</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, find the square root of 49/81, which is 7/9.</p>
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<p>First, find the square root of 49/81, which is 7/9.</p>
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<p>Then multiply by 5. (7/9) × 5 = 35/9.</p>
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<p>Then multiply by 5. (7/9) × 5 = 35/9.</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 (49/81 + 1)?</p>
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<p>What will be the square root of (49/81 + 1)?</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 4/3.</p>
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<p>The square root is 4/3.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Sum the fraction with 1: (49/81 + 81/81) = 130/81.</p>
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<p>Sum the fraction with 1: (49/81 + 81/81) = 130/81.</p>
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<p>Now, find the square root: √(130/81) ≈ 4/3.</p>
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<p>Now, find the square root: √(130/81) ≈ 4/3.</p>
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<p>Therefore, the square root of (49/81 + 1) is approximately ±4/3.</p>
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<p>Therefore, the square root of (49/81 + 1) is approximately ±4/3.</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 √(49/81) units and the width ‘w’ is 38 units.</p>
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<p>Find the perimeter of a rectangle if its length ‘l’ is √(49/81) 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 85.56 units.</p>
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<p>We find the perimeter of the rectangle as 85.56 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 × (7/9 + 38) = 2 × (0.778 + 38) = 2 × 38.778 = 77.556 units.</p>
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<p>Perimeter = 2 × (7/9 + 38) = 2 × (0.778 + 38) = 2 × 38.778 = 77.556 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 49/81</h2>
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<h2>FAQ on Square Root of 49/81</h2>
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<h3>1.What is √(49/81) in its simplest form?</h3>
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<h3>1.What is √(49/81) in its simplest form?</h3>
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<p>The simplest form of √(49/81) is 7/9, as both the numerator and the denominator are perfect squares.</p>
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<p>The simplest form of √(49/81) is 7/9, as both the numerator and the denominator are perfect squares.</p>
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<h3>2.Mention the factors of 49 and 81.</h3>
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<h3>2.Mention the factors of 49 and 81.</h3>
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<p>Factors of 49 are 1, 7, and 49. Factors of 81 are 1, 3, 9, 27, and 81.</p>
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<p>Factors of 49 are 1, 7, and 49. Factors of 81 are 1, 3, 9, 27, and 81.</p>
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<h3>3.Calculate the square of 49/81.</h3>
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<h3>3.Calculate the square of 49/81.</h3>
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<p>To find the square of 49/81, multiply the fraction by itself: (49/81) × (49/81) = 2401/6561.</p>
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<p>To find the square of 49/81, multiply the fraction by itself: (49/81) × (49/81) = 2401/6561.</p>
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<h3>4.Is 49/81 a perfect square?</h3>
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<h3>4.Is 49/81 a perfect square?</h3>
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<p>Yes, 49/81 is a perfect square because both 49 and 81 are perfect squares.</p>
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<p>Yes, 49/81 is a perfect square because both 49 and 81 are perfect squares.</p>
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<h3>5.What are the prime factors of 49 and 81?</h3>
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<h3>5.What are the prime factors of 49 and 81?</h3>
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<p>The prime factors of 49 are 7 × 7. The prime factors of 81 are 3 × 3 × 3 × 3.</p>
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<p>The prime factors of 49 are 7 × 7. The prime factors of 81 are 3 × 3 × 3 × 3.</p>
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<h2>Important Glossaries for the Square Root of 49/81</h2>
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<h2>Important Glossaries for the Square Root of 49/81</h2>
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<ul><li><strong>Square root:</strong>A square root is the operation that finds a value that, when multiplied by itself, gives the original number. Example: The square root of 16 is 4 because 4 × 4 = 16.</li>
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<ul><li><strong>Square root:</strong>A square root is the operation that finds a value that, when multiplied by itself, gives the original number. Example: The square root of 16 is 4 because 4 × 4 = 16.</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number can be expressed as the ratio of two integers, where the denominator is not zero.</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number can be expressed as the ratio of two integers, where the denominator is not zero.</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 9 is a perfect square because it is 3².</li>
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</ul><ul><li><strong>Perfect square:</strong>A perfect square is an integer that is the square of an integer. For example, 9 is a perfect square because it is 3².</li>
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</ul><ul><li><strong>Fraction:</strong>A fraction represents a part of a whole or a division of quantities. It is expressed as a numerator over a denominator, like 3/4.</li>
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</ul><ul><li><strong>Fraction:</strong>A fraction represents a part of a whole or a division of quantities. It is expressed as a numerator over a denominator, like 3/4.</li>
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</ul><ul><li><strong>Exponent:</strong>An exponent refers to the number of times a number is multiplied by itself. In the expression 2³, 3 is the exponent, indicating 2 is used as a factor three times: 2 × 2 × 2.</li>
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</ul><ul><li><strong>Exponent:</strong>An exponent refers to the number of times a number is multiplied by itself. In the expression 2³, 3 is the exponent, indicating 2 is used as a factor three times: 2 × 2 × 2.</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>