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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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 16/49.</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 various fields such as vehicle design, finance, etc. Here, we will discuss the square root of 16/49.</p>
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<h2>What is the Square Root of 16/49?</h2>
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<h2>What is the Square Root of 16/49?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. The<a>fraction</a>16/49 is a<a>perfect square</a>. The square root of 16/49 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √(16/49), whereas in exponential form it is (16/49)^(1/2). √(16/49) = 4/7, which is a<a>rational number</a>because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.</p>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of a<a>number</a>. The<a>fraction</a>16/49 is a<a>perfect square</a>. The square root of 16/49 is expressed in both radical and<a>exponential form</a>. In radical form, it is expressed as √(16/49), whereas in exponential form it is (16/49)^(1/2). √(16/49) = 4/7, which is a<a>rational number</a>because it can be expressed in the form of p/q, where p and q are integers and q ≠ 0.</p>
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<h2>Finding the Square Root of 16/49</h2>
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<h2>Finding the Square Root of 16/49</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. Since 16/49 is a perfect square, we can use the prime factorization method as well as recognizing perfect squares directly. Let's explore the following methods:</p>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. Since 16/49 is a perfect square, we can use the prime factorization method as well as recognizing perfect squares directly. Let's explore 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>Recognizing perfect squares</li>
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<li>Recognizing perfect squares</li>
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</ul><h3>Square Root of 16/49 by Prime Factorization Method</h3>
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</ul><h3>Square Root of 16/49 by Prime Factorization Method</h3>
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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 16/49 is broken down into its 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 16/49 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 16 and 49. For 16, the prime factors are 2 x 2 x 2 x 2 = 2^4. For 49, the prime factors are 7 x 7 = 7^2.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 16 and 49. For 16, the prime factors are 2 x 2 x 2 x 2 = 2^4. For 49, the prime factors are 7 x 7 = 7^2.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors. The<a>square root</a>of 16/49 is √(2^4/7^2) = (2^2/7) = 4/7.</p>
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<p><strong>Step 2:</strong>Now we found out the prime factors. The<a>square root</a>of 16/49 is √(2^4/7^2) = (2^2/7) = 4/7.</p>
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<h3>Square Root of 16/49 by Recognizing Perfect Squares</h3>
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<h3>Square Root of 16/49 by Recognizing Perfect Squares</h3>
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<p>Recognizing perfect squares is an easier method for finding the square roots of fractions that are perfect squares. Let us now learn how to find the square root using this method, step by step.</p>
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<p>Recognizing perfect squares is an easier method for finding the square roots of fractions that are perfect squares. Let us now learn how to find the square root using this method, step by step.</p>
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<p><strong>Step 1:</strong>Identify the perfect squares in the<a>numerator</a>and the<a>denominator</a>. 16 is a perfect square, as it is 4^2. 49 is a perfect square, as it is 7^2.</p>
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<p><strong>Step 1:</strong>Identify the perfect squares in the<a>numerator</a>and the<a>denominator</a>. 16 is a perfect square, as it is 4^2. 49 is a perfect square, as it is 7^2.</p>
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<p><strong>Step 2:</strong>The square root of 16/49 is simply the square root of the numerator over the square root of the denominator, which is 4/7.</p>
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<p><strong>Step 2:</strong>The square root of 16/49 is simply the square root of the numerator over the square root of the denominator, which is 4/7.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 16/49</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 16/49</h2>
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<p>Students do make mistakes while finding the square root, like forgetting about the negative square root or incorrectly applying the square root to fractions. 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 or incorrectly applying the square root to fractions. 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 √(16/49)?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √(16/49)?</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 area of the square is 16/49 square units.</p>
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<p>The area of the square is 16/49 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 √(16/49).</p>
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<p>The side length is given as √(16/49).</p>
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<p>Area of the square = side² = (4/7) × (4/7) = 16/49.</p>
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<p>Area of the square = side² = (4/7) × (4/7) = 16/49.</p>
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<p>Therefore, the area of the square box is 16/49 square units.</p>
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<p>Therefore, the area of the square box is 16/49 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 16/49 square feet is built; if each of the sides is √(16/49), what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 16/49 square feet is built; if each of the sides is √(16/49), 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>8/49 square feet</p>
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<p>8/49 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 16/49 by 2 = 8/49.</p>
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<p>Dividing 16/49 by 2 = 8/49.</p>
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<p>So half of the building measures 8/49 square feet.</p>
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<p>So half of the building measures 8/49 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 √(16/49) × 5.</p>
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<p>Calculate √(16/49) × 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>20/7</p>
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<p>20/7</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 16/49, which is 4/7.</p>
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<p>The first step is to find the square root of 16/49, which is 4/7.</p>
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<p>The second step is to multiply 4/7 by 5.</p>
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<p>The second step is to multiply 4/7 by 5.</p>
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<p>So (4/7) × 5 = 20/7.</p>
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<p>So (4/7) × 5 = 20/7.</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 (16/49 + 1)?</p>
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<p>What will be the square root of (16/49 + 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 8/7.</p>
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<p>The square root is 8/7.</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 (16/49 + 1).</p>
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<p>To find the square root, we need to find the sum of (16/49 + 1).</p>
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<p>16/49 + 49/49 = 65/49, and then √(65/49) = 8/7.</p>
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<p>16/49 + 49/49 = 65/49, and then √(65/49) = 8/7.</p>
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<p>Therefore, the square root of (16/49 + 1) is 8/7.</p>
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<p>Therefore, the square root of (16/49 + 1) is 8/7.</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 √(16/49) 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 √(16/49) 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>The perimeter of the rectangle is 76 + 8/7 units.</p>
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<p>The perimeter of the rectangle is 76 + 8/7 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 × (√(16/49) + 38) = 2 × (4/7 + 38) = 2 × (4/7 + 266/7) = 2 × 270/7 = 540/7 = 76 + 8/7 units.</p>
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<p>Perimeter = 2 × (√(16/49) + 38) = 2 × (4/7 + 38) = 2 × (4/7 + 266/7) = 2 × 270/7 = 540/7 = 76 + 8/7 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 16/49</h2>
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<h2>FAQ on Square Root of 16/49</h2>
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<h3>1.What is √(16/49) in its simplest form?</h3>
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<h3>1.What is √(16/49) in its simplest form?</h3>
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<p>The simplest form of √(16/49) is 4/7, as both 16 and 49 are perfect squares.</p>
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<p>The simplest form of √(16/49) is 4/7, as both 16 and 49 are perfect squares.</p>
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<h3>2.Mention the factors of 16/49.</h3>
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<h3>2.Mention the factors of 16/49.</h3>
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<p>Factors of 16/49 are derived from its<a>numerator and denominator</a>. For 16, factors are 1, 2, 4, 8, 16. For 49, factors are 1, 7, 49.</p>
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<p>Factors of 16/49 are derived from its<a>numerator and denominator</a>. For 16, factors are 1, 2, 4, 8, 16. For 49, factors are 1, 7, 49.</p>
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<h3>3.Calculate the square of 16/49.</h3>
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<h3>3.Calculate the square of 16/49.</h3>
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<p>We get the square of 16/49 by multiplying the number by itself: (16/49) × (16/49) = 256/2401.</p>
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<p>We get the square of 16/49 by multiplying the number by itself: (16/49) × (16/49) = 256/2401.</p>
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<h3>4.Is 16/49 a prime number?</h3>
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<h3>4.Is 16/49 a prime number?</h3>
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<p>16/49 is not a<a>prime number</a>, as it is a fraction composed of two non-prime numbers.</p>
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<p>16/49 is not a<a>prime number</a>, as it is a fraction composed of two non-prime numbers.</p>
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<h3>5.16/49 is divisible by?</h3>
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<h3>5.16/49 is divisible by?</h3>
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<p>16/49 is a fraction, so it is divisible by its own factors, which are the factors of 16 and 49. Factors include numbers like 1/49, 2/49, 4/49, 8/49, and 16/49 itself.</p>
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<p>16/49 is a fraction, so it is divisible by its own factors, which are the factors of 16 and 49. Factors include numbers like 1/49, 2/49, 4/49, 8/49, and 16/49 itself.</p>
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<h2>Important Glossaries for the Square Root of 16/49</h2>
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<h2>Important Glossaries for the Square Root of 16/49</h2>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, 4² = 16, and the square root is √16 = 4.</li>
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<ul><li><strong>Square root:</strong>A square root is the inverse operation of squaring a number. For example, 4² = 16, and the square root is √16 = 4.</li>
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</ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.<strong></strong></li>
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</ul><ul><li><strong>Rational number:</strong>A rational number is a number that can be expressed in the form of p/q, where q is not equal to zero and p and q are integers.<strong></strong></li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 16 and 49 are perfect squares.<strong></strong></li>
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</ul><ul><li><strong>Perfect square:</strong>A number that is the square of an integer. For example, 16 and 49 are perfect squares.<strong></strong></li>
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</ul><ul><li><strong>Fraction:</strong>A numerical quantity that is not a whole number, represented by two numbers, one above the other and separated by a line, for example, 3/4.</li>
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</ul><ul><li><strong>Fraction:</strong>A numerical quantity that is not a whole number, represented by two numbers, one above the other and separated by a line, for example, 3/4.</li>
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</ul><ul><li><strong>Reciprocal:</strong>The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of 4/7 is 7/4.</li>
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</ul><ul><li><strong>Reciprocal:</strong>The reciprocal of a fraction is obtained by swapping the numerator and the denominator. For example, the reciprocal of 4/7 is 7/4.</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>