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Original
2026-01-01
Modified
2026-02-28
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<p>The long<a>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 square root using the long division method, step by step.</p>
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<p>The long<a>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 square root 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 1037, we need to group it as 37 and 10.</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 1037, we need to group it as 37 and 10.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is closest to 10. We can say n is '3' because 3×3 = 9 is lesser than 10. Now the<a>quotient</a>is 3, and after subtracting 9 from 10, 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 closest to 10. We can say n is '3' because 3×3 = 9 is lesser than 10. Now the<a>quotient</a>is 3, and after subtracting 9 from 10, the<a>remainder</a>is 1.</p>
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<p><strong>Step 3:</strong>Now let us bring down 37, making the new<a>dividend</a>137. Add the old<a>divisor</a>with the same number: 3+3=6, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 37, making the new<a>dividend</a>137. Add the old<a>divisor</a>with the same number: 3+3=6, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor is 6n. We need to find n such that 6n × n ≤ 137. Let us consider n as 2, now 62×2 = 124.</p>
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<p><strong>Step 4:</strong>The new divisor is 6n. We need to find n such that 6n × n ≤ 137. Let us consider n as 2, now 62×2 = 124.</p>
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<p><strong>Step 5:</strong>Subtract 124 from 137, the difference is 13, and the quotient is 32.</p>
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<p><strong>Step 5:</strong>Subtract 124 from 137, the difference is 13, and the quotient is 32.</p>
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<p><strong>Step 6:</strong>Since the dividend is<a>less than</a>the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1300.</p>
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<p><strong>Step 6:</strong>Since the dividend is<a>less than</a>the divisor, we need to add a<a>decimal</a>point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1300.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 644 because 644×2 = 1288.</p>
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<p><strong>Step 7:</strong>Now we need to find the new divisor, which is 644 because 644×2 = 1288.</p>
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<p><strong>Step 8:</strong>Subtracting 1288 from 1300, we get the result of 12.</p>
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<p><strong>Step 8:</strong>Subtracting 1288 from 1300, we get the result of 12.</p>
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<p><strong>Step 9:</strong>The quotient now is 32.2.</p>
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<p><strong>Step 9:</strong>The quotient now is 32.2.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue until the remainder is zero.</p>
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<p><strong>Step 10:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal value, continue until the remainder is zero.</p>
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<p>So the square root of √1037 is approximately 32.218.</p>
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<p>So the square root of √1037 is approximately 32.218.</p>
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