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Original
2026-01-01
Modified
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 with, we need to group the numbers from right to left. In the case of 9375, we need to group it as 75 and 93.</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 9375, we need to group it as 75 and 93.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤93. We can say n as ‘9’ because 9 x 9 is<a>less than</a>or equal to 93. Now the<a>quotient</a>is 9; after subtracting 81 from 93, the<a>remainder</a>is 12.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is ≤93. We can say n as ‘9’ because 9 x 9 is<a>less than</a>or equal to 93. Now the<a>quotient</a>is 9; after subtracting 81 from 93, the<a>remainder</a>is 12.</p>
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<p><strong>Step 3:</strong>Now let us bring down 75, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 9 + 9; we get 18, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 75, which is the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 9 + 9; we get 18, 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 18n 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 18n 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 18n x n ≤ 1275. Let us consider n as 7. Now, 18 x 7 x 7 = 1764. Since 1764 is greater than 1275, try n as 6.</p>
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<p><strong>Step 5:</strong>The next step is finding 18n x n ≤ 1275. Let us consider n as 7. Now, 18 x 7 x 7 = 1764. Since 1764 is greater than 1275, try n as 6.</p>
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<p><strong>Step 6:</strong>With n as 6, 18 x 6 x 6 = 1296. Subtracting 1296 from 1275 is not possible as 1296 is greater, so n has to be decreased.</p>
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<p><strong>Step 6:</strong>With n as 6, 18 x 6 x 6 = 1296. Subtracting 1296 from 1275 is not possible as 1296 is greater, so n has to be decreased.</p>
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<p><strong>Step 7:</strong>With n as 5, 18 x 5 x 5 = 1125. Subtract 1125 from 1275; the difference is 150, and the quotient is 95.</p>
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<p><strong>Step 7:</strong>With n as 5, 18 x 5 x 5 = 1125. Subtract 1125 from 1275; the difference is 150, and the quotient is 95.</p>
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<p><strong>Step 8:</strong>Now, since the number of digits in the dividend is less than the divisor, we add a decimal point to continue with zeros. Now, the new dividend is 15000.</p>
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<p><strong>Step 8:</strong>Now, since the number of digits in the dividend is less than the divisor, we add a decimal point to continue with zeros. Now, the new dividend is 15000.</p>
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<p><strong>Step 9:</strong>The next divisor is 1950, as 195 x 9 = 1755.</p>
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<p><strong>Step 9:</strong>The next divisor is 1950, as 195 x 9 = 1755.</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 till 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 till the remainder is zero.</p>
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<p>So, the square root of √9375 ≈ 96.87</p>
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<p>So, the square root of √9375 ≈ 96.87</p>
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