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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<a>square root</a>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<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 6900, we need to group it as 00 and 69.</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 6900, we need to group it as 00 and 69.</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 69. We can say n is ‘8’ because 8 × 8 = 64 is lesser than 69. Now the<a>quotient</a>is 8, and after subtracting 64 from 69, the<a>remainder</a>is 5.</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 69. We can say n is ‘8’ because 8 × 8 = 64 is lesser than 69. Now the<a>quotient</a>is 8, and after subtracting 64 from 69, the<a>remainder</a>is 5.</p>
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<p><strong>Step 3:</strong>Now let us bring down 00 to make the new<a>dividend</a>500. Add the old<a>divisor</a>with the same number 8 + 8 to get 16, which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 00 to make the new<a>dividend</a>500. Add the old<a>divisor</a>with the same number 8 + 8 to get 16, 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. We get 16n as the new divisor, and 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. We get 16n as the new divisor, and we need to find the value of n.</p>
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<p><strong>Step 5:</strong>The next step is finding 16n × n ≤ 500. Let us consider n as 3, now 16 × 3 × 3 = 489.</p>
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<p><strong>Step 5:</strong>The next step is finding 16n × n ≤ 500. Let us consider n as 3, now 16 × 3 × 3 = 489.</p>
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<p><strong>Step 6:</strong>Subtract 489 from 500, the difference is 11, and the quotient is 83.</p>
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<p><strong>Step 6:</strong>Subtract 489 from 500, the difference is 11, and the quotient is 83.</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 1100.</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 1100.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. If we consider the new digit as 6, then 1666 × 6 = 9996.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor. If we consider the new digit as 6, then 1666 × 6 = 9996.</p>
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<p><strong>Step 9:</strong>Subtracting 9996 from 11000, we get the result 1004.</p>
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<p><strong>Step 9:</strong>Subtracting 9996 from 11000, we get the result 1004.</p>
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<p><strong>Step 10:</strong>Now the quotient is 83.0</p>
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<p><strong>Step 10:</strong>Now the quotient is 83.0</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 until the remainder is zero. So the square root of √6900 is approximately 83.045.</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 until the remainder is zero. So the square root of √6900 is approximately 83.045.</p>
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