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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 1744.</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 1744.</p>
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<h2>What is the Square Root of 1744?</h2>
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<h2>What is the Square Root of 1744?</h2>
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<p>The<a>square</a>root is the inverse of the square of the<a>number</a>. 1744 is not a<a>perfect square</a>. The square root of 1744 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1744, whereas (1744)^(1/2) in the exponential form. √1744 ≈ 41.758, 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 of the square of the<a>number</a>. 1744 is not a<a>perfect square</a>. The square root of 1744 is expressed in both radical and<a>exponential form</a>. In the radical form, it is expressed as √1744, whereas (1744)^(1/2) in the exponential form. √1744 ≈ 41.758, 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 1744</h2>
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<h2>Finding the Square Root of 1744</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 1744 by Prime Factorization Method</h2>
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</ul><h2>Square Root of 1744 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 1744 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 1744 is broken down into its prime factors.</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1744 Breaking it down, we get 2 x 2 x 2 x 2 x 109: 2^4 x 109^1</p>
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<p><strong>Step 1:</strong>Finding the prime factors of 1744 Breaking it down, we get 2 x 2 x 2 x 2 x 109: 2^4 x 109^1</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 1744. The second step is to make pairs of those prime factors. Since 1744 is not a perfect square, the digits of the number can’t be grouped in pairs to form a perfect square.</p>
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<p><strong>Step 2:</strong>Now we have found the prime factors of 1744. The second step is to make pairs of those prime factors. Since 1744 is not a perfect square, the digits of the number can’t be grouped in pairs to form a perfect square.</p>
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<p>Therefore, calculating √1744 using prime factorization requires approximation.</p>
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<p>Therefore, calculating √1744 using prime factorization requires approximation.</p>
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<h2>Square Root of 1744 by Long Division Method</h2>
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<h2>Square Root of 1744 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>To begin with, we need to group the numbers from right to left. In the case of 1744, we need to group it as 44 and 17.</p>
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<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1744, we need to group it as 44 and 17.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 17. We can say n is ‘4’ because 4 x 4 = 16 is<a>less than</a>or equal to 17. Now the<a>quotient</a>is 4, and after subtracting 16 from 17, the<a>remainder</a>is 1.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤ 17. We can say n is ‘4’ because 4 x 4 = 16 is<a>less than</a>or equal to 17. Now the<a>quotient</a>is 4, and after subtracting 16 from 17, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 44, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 4 + 4 = 8, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 44, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 4 + 4 = 8, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be 8n, and we need to find the value of n such that 8n x n ≤ 144. Let us consider n as 1, now 81 x 1 = 81.</p>
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<p><strong>Step 4:</strong>The new divisor will be 8n, and we need to find the value of n such that 8n x n ≤ 144. Let us consider n as 1, now 81 x 1 = 81.</p>
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<p><strong>Step 5:</strong>Subtract 81 from 144, the difference is 63, and the quotient is 41.</p>
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<p><strong>Step 5:</strong>Subtract 81 from 144, the difference is 63, and the quotient is 41.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 6300.</p>
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<p><strong>Step 6:</strong>Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 6300.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 418 because 418 x 8 = 3344.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 418 because 418 x 8 = 3344.</p>
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<p><strong>Step 8:</strong>Subtracting 3344 from 6300, we get the result 2956.</p>
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<p><strong>Step 8:</strong>Subtracting 3344 from 6300, we get the result 2956.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get the desired number of decimal places.</p>
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<p><strong>Step 9:</strong>Continue doing these steps until we get the desired number of decimal places.</p>
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<p>So the square root of √1744 is approximately 41.758.</p>
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<p>So the square root of √1744 is approximately 41.758.</p>
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<h2>Square Root of 1744 by Approximation Method</h2>
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<h2>Square Root of 1744 by Approximation Method</h2>
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<p>The approximation method is another method for finding 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 1744 using the approximation method.</p>
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<p>The approximation method is another method for finding 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 1744 using the approximation method.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square to √1744.</p>
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<p><strong>Step 1:</strong>Now we have to find the closest perfect square to √1744.</p>
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<p>The smallest perfect square less than 1744 is 1600, and the largest perfect square<a>greater than</a>1744 is 1764.</p>
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<p>The smallest perfect square less than 1744 is 1600, and the largest perfect square<a>greater than</a>1744 is 1764.</p>
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<p>√1744 falls somewhere between 40 and 42.</p>
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<p>√1744 falls somewhere between 40 and 42.</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>:</p>
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<p><strong>Step 2:</strong>Now we need to apply the<a>formula</a>:</p>
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<p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
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<p>(Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).</p>
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<p>Going by the formula: (1744 - 1600) / (1764 - 1600) = 144 / 164 ≈ 0.878.</p>
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<p>Going by the formula: (1744 - 1600) / (1764 - 1600) = 144 / 164 ≈ 0.878.</p>
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<p>Using the formula, we identified the<a>decimal</a>point of our square root.</p>
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<p>Using the formula, we identified the<a>decimal</a>point of our square root.</p>
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<p>The next step is adding the integer part, which is 40, to the decimal number we found: 40 + 0.878 = 40.878.</p>
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<p>The next step is adding the integer part, which is 40, to the decimal number we found: 40 + 0.878 = 40.878.</p>
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<p>Thus, the approximate square root of 1744 is 40.878.</p>
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<p>Thus, the approximate square root of 1744 is 40.878.</p>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1744</h2>
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<h2>Common Mistakes and How to Avoid Them in the Square Root of 1744</h2>
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<p>Students do 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 do 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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<h2>Download Worksheets</h2>
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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 √1444?</p>
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<p>Can you help Max find the area of a square box if its side length is given as √1444?</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 1444 square units.</p>
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<p>The area of the square is 1444 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. The side length is given as √1444. Area of the square = side^2 = √1444 x √1444 = 38 x 38 = 1444. Therefore, the area of the square box is 1444 square units.</p>
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<p>The area of the square = side^2. The side length is given as √1444. Area of the square = side^2 = √1444 x √1444 = 38 x 38 = 1444. Therefore, the area of the square box is 1444 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 1744 square feet is built; if each of the sides is √1744, what will be the square feet of half of the building?</p>
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<p>A square-shaped building measuring 1744 square feet is built; if each of the sides is √1744, 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>872 square feet</p>
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<p>872 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. Dividing 1744 by 2 = we get 872. So half of the building measures 872 square feet.</p>
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<p>We can just divide the given area by 2 as the building is square-shaped. Dividing 1744 by 2 = we get 872. So half of the building measures 872 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 √1744 x 5.</p>
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<p>Calculate √1744 x 5.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>208.79</p>
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<p>208.79</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 1744, which is approximately 41.758. The second step is to multiply 41.758 by 5. So 41.758 x 5 ≈ 208.79.</p>
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<p>The first step is to find the square root of 1744, which is approximately 41.758. The second step is to multiply 41.758 by 5. So 41.758 x 5 ≈ 208.79.</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 (1444 + 300)?</p>
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<p>What will be the square root of (1444 + 300)?</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 42.66.</p>
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<p>The square root is approximately 42.66.</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 (1444 + 300). 1444 + 300 = 1744, and then √1744 ≈ 41.758. Therefore, the square root of (1444 + 300) is approximately 41.758.</p>
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<p>To find the square root, we need to find the sum of (1444 + 300). 1444 + 300 = 1744, and then √1744 ≈ 41.758. Therefore, the square root of (1444 + 300) is approximately 41.758.</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 √1444 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 √1444 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 152 units.</p>
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<p>We find the perimeter of the rectangle as 152 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). Perimeter = 2 × (√1444 + 38) = 2 × (38 + 38) = 2 × 76 = 152 units.</p>
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<p>Perimeter of the rectangle = 2 × (length + width). Perimeter = 2 × (√1444 + 38) = 2 × (38 + 38) = 2 × 76 = 152 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 1744</h2>
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<h2>FAQ on Square Root of 1744</h2>
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<h3>1.What is √1744 in its simplest form?</h3>
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<h3>1.What is √1744 in its simplest form?</h3>
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<p>The prime factorization of 1744 is 2 x 2 x 2 x 2 x 109, so the simplest form of √1744 is √(2^4 x 109).</p>
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<p>The prime factorization of 1744 is 2 x 2 x 2 x 2 x 109, so the simplest form of √1744 is √(2^4 x 109).</p>
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<h3>2.Mention the factors of 1744.</h3>
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<h3>2.Mention the factors of 1744.</h3>
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<p>Factors of 1744 are 1, 2, 4, 8, 16, 109, 218, 436, 872, and 1744.</p>
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<p>Factors of 1744 are 1, 2, 4, 8, 16, 109, 218, 436, 872, and 1744.</p>
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<h3>3.Calculate the square of 1744.</h3>
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<h3>3.Calculate the square of 1744.</h3>
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<p>We get the square of 1744 by multiplying the number by itself, that is 1744 x 1744 = 3,042,816.</p>
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<p>We get the square of 1744 by multiplying the number by itself, that is 1744 x 1744 = 3,042,816.</p>
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<h3>4.Is 1744 a prime number?</h3>
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<h3>4.Is 1744 a prime number?</h3>
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<p>1744 is not a<a>prime number</a>, as it has more than two factors.</p>
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<p>1744 is not a<a>prime number</a>, as it has more than two factors.</p>
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<h3>5.1744 is divisible by?</h3>
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<h3>5.1744 is divisible by?</h3>
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<p>1744 has several factors; those are 1, 2, 4, 8, 16, 109, 218, 436, 872, and 1744.</p>
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<p>1744 has several factors; those are 1, 2, 4, 8, 16, 109, 218, 436, 872, and 1744.</p>
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<h2>Important Glossaries for the Square Root of 1744</h2>
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<h2>Important Glossaries for the Square Root of 1744</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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<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>Prime factorization:</strong>Breaking down a number into its basic prime number factors. </li>
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<li><strong>Prime factorization:</strong>Breaking down a number into its basic prime number factors. </li>
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<li><strong>Long division method:</strong>A step-by-step process of dividing a number to find its square root, especially useful for non-perfect squares. </li>
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<li><strong>Long division method:</strong>A step-by-step process of dividing a number to find its square root, especially useful for non-perfect squares. </li>
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<li><strong>Approximation method:</strong>A method used to estimate the square root of a number by comparing it to the nearest perfect squares.</li>
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<li><strong>Approximation method:</strong>A method used to estimate the square root of a number by comparing it to the nearest perfect squares.</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>