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Original
2026-01-01
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2026-02-28
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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, we need to group the numbers from right to left. In the case of 1762, we need to group it as 62 and 17.</p>
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<p><strong>Step 1:</strong>To begin, we need to group the numbers from right to left. In the case of 1762, we need to group it as 62 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 × 4 = 16, which is<a>less than</a>or equal to 17. Now the<a>quotient</a>is 4. 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 × 4 = 16, which is<a>less than</a>or equal to 17. Now the<a>quotient</a>is 4. 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 62, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 4 + 4, we get 8, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 62, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 4 + 4, we get 8, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor; we need to find the value of n.</p>
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<p><strong>Step 4:</strong>The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor; we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 8n × n ≤ 162. Let us consider n as 2, now 82 × 2 = 164, which is too large. Let's try n = 1, so 81 × 1 = 81.</p>
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<p><strong>Step 5:</strong>The next step is finding 8n × n ≤ 162. Let us consider n as 2, now 82 × 2 = 164, which is too large. Let's try n = 1, so 81 × 1 = 81.</p>
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<p><strong>Step 6:</strong>Subtract 81 from 162, the difference is 81, and the quotient is 41.</p>
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<p><strong>Step 6:</strong>Subtract 81 from 162, the difference is 81, and the quotient is 41.</p>
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<p><strong>Step 7:</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 zeroes to the dividend. Now the new dividend is 8100.</p>
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<p><strong>Step 7:</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 zeroes to the dividend. Now the new dividend is 8100.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 829 because 829 × 9 = 7461.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 829 because 829 × 9 = 7461.</p>
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<p><strong>Step 9:</strong>Subtracting 7461 from 8100, we get the result 639.</p>
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<p><strong>Step 9:</strong>Subtracting 7461 from 8100, we get the result 639.</p>
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<p><strong>Step 10:</strong>Now the quotient is 41.9.</p>
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<p><strong>Step 10:</strong>Now the quotient is 41.9.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.</p>
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<p>So the square root of √1762 is approximately 41.98.</p>
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<p>So the square root of √1762 is approximately 41.98.</p>
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