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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 9225, we need to group it as 25 and 92.</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 9225, we need to group it as 25 and 92.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 92. We can say n is ‘9’ because 9 x 9 = 81, which is less than 92. Now the<a>quotient</a>is 9, and after subtracting 81 from 92, the<a>remainder</a>is 11.</p>
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<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 92. We can say n is ‘9’ because 9 x 9 = 81, which is less than 92. Now the<a>quotient</a>is 9, and after subtracting 81 from 92, the<a>remainder</a>is 11.</p>
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<p><strong>Step 3:</strong>Now, let us bring down 25, which becomes the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 9 + 9 to get 18, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now, let us bring down 25, which becomes the new<a>dividend</a>. Add the old<a>divisor</a>with the same number 9 + 9 to get 18, which will be our new divisor.</p>
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<p><strong>Step 4:</strong>The new divisor will be represented as 18n. We need to find the value of n such that 18n x n ≤ 1125.</p>
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<p><strong>Step 4:</strong>The new divisor will be represented as 18n. We need to find the value of n such that 18n x n ≤ 1125.</p>
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<p><strong>Step 5:</strong>The next step is finding 18n × n ≤ 1125. Let us consider n as 6, now 186 x 6 = 1116.</p>
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<p><strong>Step 5:</strong>The next step is finding 18n × n ≤ 1125. Let us consider n as 6, now 186 x 6 = 1116.</p>
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<p><strong>Step 6:</strong>Subtract 1116 from 1125; the difference is 9, and the quotient becomes 96.</p>
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<p><strong>Step 6:</strong>Subtract 1116 from 1125; the difference is 9, and the quotient becomes 96.</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 900.</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 900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 193, because 193 x 4 = 772.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor, which is 193, because 193 x 4 = 772.</p>
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<p><strong>Step 9:</strong>Subtracting 772 from 900, we get the result 128.</p>
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<p><strong>Step 9:</strong>Subtracting 772 from 900, we get the result 128.</p>
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<p><strong>Step 10:</strong>Now the quotient is 96.0.</p>
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<p><strong>Step 10:</strong>Now the quotient is 96.0.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>
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<p><strong>Step 11:</strong>Continue doing these steps until we get two numbers after the decimal point.</p>
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<p>So the square root of √9225 is approximately 96.06.</p>
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<p>So the square root of √9225 is approximately 96.06.</p>
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