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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 such as vehicle design, finance, etc. Here, we will discuss the square root of 14.5.</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 14.5.</p>
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<h2>What is the Square Root of 14.5?</h2>
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<h2>What is the Square Root of 14.5?</h2>
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<p>The<a>square</a>root is the inverse<a>of</a>the square of the<a>number</a>. 14.5 is not a<a>perfect square</a>. The square root of 14.5 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √14.5, whereas (14.5)^(1/2) in the exponential form. √14.5 ≈ 3.8079, which is an<a>irrational number</a>because it cannot 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>. 14.5 is not a<a>perfect square</a>. The square root of 14.5 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √14.5, whereas (14.5)^(1/2) in the exponential form. √14.5 ≈ 3.8079, which is an<a>irrational number</a>because it cannot 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 14.5</h2>
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<h2>Finding the Square Root of 14.5</h2>
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<p>The<a>prime factorization</a>method is used for perfect square numbers. However, the prime factorization method is not used for non-perfect square numbers where the long-<a>division</a>method and approximation method are used. 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. However, the prime factorization method is not used for non-perfect square numbers where the long-<a>division</a>method and approximation method are used. 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>Long division method</li>
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<li>Long division method</li>
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<li>Approximation method</li>
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<li>Approximation method</li>
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</ul><h2>Square Root of 14.5 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 14.5 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. However, since 14.5 is not a perfect square and is a<a>decimal</a>, the prime factorization method cannot be directly applied as it is with<a>whole numbers</a>.</p>
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<p>The<a>product</a>of prime<a>factors</a>is the prime factorization of a number. However, since 14.5 is not a perfect square and is a<a>decimal</a>, the prime factorization method cannot be directly applied as it is with<a>whole numbers</a>.</p>
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<h2>Square Root of 14.5 by Long Division Method</h2>
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<h2>Square Root of 14.5 by Long Division Method</h2>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>
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<p>The<a>long division</a>method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the<a>square root</a>using the long division method, step by step.</p>
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<p><strong>Step 1:</strong>Group the numbers from right to left. For 14.5, it's already a single number.</p>
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<p><strong>Step 1:</strong>Group the numbers from right to left. For 14.5, it's already a single number.</p>
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<p><strong>Step 2:</strong>Identify a number n whose square is closest to 1. The closest perfect square is 1 (1×1), so the first digit of the<a>quotient</a>is 1.</p>
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<p><strong>Step 2:</strong>Identify a number n whose square is closest to 1. The closest perfect square is 1 (1×1), so the first digit of the<a>quotient</a>is 1.</p>
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<p><strong>Step 3:</strong>Subtract to get the<a>remainder</a>and bring down the decimal part to work with 450.</p>
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<p><strong>Step 3:</strong>Subtract to get the<a>remainder</a>and bring down the decimal part to work with 450.</p>
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<p><strong>Step 4:</strong>Double the current quotient (1) to get 2, which will be used as the new<a>divisor</a>'s first digit.</p>
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<p><strong>Step 4:</strong>Double the current quotient (1) to get 2, which will be used as the new<a>divisor</a>'s first digit.</p>
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<p><strong>Step 5:</strong>Find a digit x such that 2x × x is<a>less than</a>or equal to 450. For x = 3, 23 × 3 = 69.</p>
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<p><strong>Step 5:</strong>Find a digit x such that 2x × x is<a>less than</a>or equal to 450. For x = 3, 23 × 3 = 69.</p>
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<p><strong>Step 6:</strong>Subtract 69 from 450 to get 381, and continue the process to get the decimal places.</p>
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<p><strong>Step 6:</strong>Subtract 69 from 450 to get 381, and continue the process to get the decimal places.</p>
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<p>Continue the steps until you achieve the desired precision, leading to an approximate square root of 3.8079.</p>
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<p>Continue the steps until you achieve the desired precision, leading to an approximate square root of 3.8079.</p>
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<h2>Square Root of 14.5 by Approximation Method</h2>
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<h2>Square Root of 14.5 by Approximation Method</h2>
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<p>The approximation 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 14.5 using the approximation method.</p>
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<p>The approximation 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 14.5 using the approximation method.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares to √14.5. The closest perfect squares are 9 (3×3) and 16 (4×4), so √14.5 is between 3 and 4.</p>
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<p><strong>Step 1:</strong>Identify the closest perfect squares to √14.5. The closest perfect squares are 9 (3×3) and 16 (4×4), so √14.5 is between 3 and 4.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square).</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square).</p>
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<p>Using the formula: (14.5 - 9) / (16 - 9) = 5.5 / 7 ≈ 0.7857</p>
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<p>Using the formula: (14.5 - 9) / (16 - 9) = 5.5 / 7 ≈ 0.7857</p>
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<p>Adding this to the lower integer: 3 + 0.7857 ≈ 3.7857</p>
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<p>Adding this to the lower integer: 3 + 0.7857 ≈ 3.7857</p>
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<p>So the square root of 14.5 is approximately 3.8079.</p>
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<p>So the square root of 14.5 is approximately 3.8079.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 14.5</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 14.5</h2>
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<p>Students can make mistakes while finding the square root, such as forgetting about the negative square root. Skipping long division 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 can make mistakes while finding the square root, such as forgetting about the negative square root. Skipping long division 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 √14.5?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √14.5?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The area of the square is approximately 14.5 square units.</p>
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<p>The area of the square is approximately 14.5 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 √14.5.</p>
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<p>The side length is given as √14.5.</p>
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<p>Area of the square = (√14.5)² = 14.5.</p>
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<p>Area of the square = (√14.5)² = 14.5.</p>
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<p>Therefore, the area of the square box is 14.5 square units.</p>
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<p>Therefore, the area of the square box is 14.5 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 garden measuring 14.5 square meters is built; if each of the sides is √14.5, what will be the square meters of half of the garden?</p>
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<p>A square-shaped garden measuring 14.5 square meters is built; if each of the sides is √14.5, what will be the square meters of half of the garden?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>7.25 square meters</p>
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<p>7.25 square meters</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We can divide the given area by 2 as the garden is square-shaped.</p>
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<p>We can divide the given area by 2 as the garden is square-shaped.</p>
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<p>Dividing 14.5 by 2, we get 7.25.</p>
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<p>Dividing 14.5 by 2, we get 7.25.</p>
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<p>So half of the garden measures 7.25 square meters.</p>
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<p>So half of the garden measures 7.25 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 √14.5 × 5.</p>
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<p>Calculate √14.5 × 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>Approximately 19.04</p>
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<p>Approximately 19.04</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 14.5, which is approximately 3.8079.</p>
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<p>The first step is to find the square root of 14.5, which is approximately 3.8079.</p>
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<p>The second step is to multiply 3.8079 by 5.</p>
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<p>The second step is to multiply 3.8079 by 5.</p>
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<p>So 3.8079 × 5 ≈ 19.04.</p>
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<p>So 3.8079 × 5 ≈ 19.04.</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 (14 + 0.5)?</p>
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<p>What will be the square root of (14 + 0.5)?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The square root is approximately 3.8079.</p>
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<p>The square root is approximately 3.8079.</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 (14 + 0.5), which is 14.5.</p>
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<p>To find the square root, we need to find the sum of (14 + 0.5), which is 14.5.</p>
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<p>Then, √14.5 ≈ 3.8079.</p>
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<p>Then, √14.5 ≈ 3.8079.</p>
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<p>Therefore, the square root of (14 + 0.5) is approximately ±3.8079.</p>
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<p>Therefore, the square root of (14 + 0.5) is approximately ±3.8079.</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 √14.5 units and the width ‘w’ is 4 units.</p>
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<p>Find the perimeter of the rectangle if its length ‘l’ is √14.5 units and the width ‘w’ is 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>We find the perimeter of the rectangle as approximately 15.62 units.</p>
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<p>We find the perimeter of the rectangle as approximately 15.62 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 × (√14.5 + 4) = 2 × (3.8079 + 4) = 2 × 7.8079 ≈ 15.62 units.</p>
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<p>Perimeter = 2 × (√14.5 + 4) = 2 × (3.8079 + 4) = 2 × 7.8079 ≈ 15.62 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 14.5</h2>
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<h2>FAQ on Square Root of 14.5</h2>
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<h3>1.What is √14.5 in its simplest form?</h3>
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<h3>1.What is √14.5 in its simplest form?</h3>
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<p>Since 14.5 is not a perfect square, √14.5 is already in its simplest radical form: √14.5.</p>
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<p>Since 14.5 is not a perfect square, √14.5 is already in its simplest radical form: √14.5.</p>
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<h3>2.Is 14.5 a perfect square?</h3>
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<h3>2.Is 14.5 a perfect square?</h3>
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<p>No, 14.5 is not a perfect square because its square root is not an integer.</p>
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<p>No, 14.5 is not a perfect square because its square root is not an integer.</p>
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<h3>3.Calculate the square of 14.5.</h3>
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<h3>3.Calculate the square of 14.5.</h3>
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<p>We get the square of 14.5 by multiplying the number by itself: 14.5 × 14.5 = 210.25.</p>
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<p>We get the square of 14.5 by multiplying the number by itself: 14.5 × 14.5 = 210.25.</p>
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<h3>4.Is 14.5 a prime number?</h3>
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<h3>4.Is 14.5 a prime number?</h3>
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<h3>5.What are the factors of 14.5?</h3>
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<h3>5.What are the factors of 14.5?</h3>
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<p>Since 14.5 is a decimal, it does not have factors in the same way that whole numbers do.</p>
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<p>Since 14.5 is a decimal, it does not have factors in the same way that whole numbers do.</p>
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<h2>Important Glossaries for the Square Root of 14.5</h2>
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<h2>Important Glossaries for the Square Root of 14.5</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, which 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, which is √16 = 4. </li>
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<li><strong>Irrational number:</strong>An irrational number is a number that cannot 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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<li><strong>Irrational number:</strong>An irrational number is a number that cannot 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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<li><strong>Decimal:</strong>A decimal is a number that includes a fractional component, such as 7.86, 8.65, and 9.42. </li>
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<li><strong>Decimal:</strong>A decimal is a number that includes a fractional component, such as 7.86, 8.65, and 9.42. </li>
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<li><strong>Approximation:</strong>The process of finding a value that is close enough to the right answer, usually with some thought or calculation involved. </li>
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<li><strong>Approximation:</strong>The process of finding a value that is close enough to the right answer, usually with some thought or calculation involved. </li>
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<li><strong>Long division method:</strong>A method used to find the square root of non-perfect squares by dividing the number into pairs and finding the most accurate quotient possible.</li>
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<li><strong>Long division method:</strong>A method used to find the square root of non-perfect squares by dividing the number into pairs and finding the most accurate quotient possible.</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>