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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 353, we need to group it as 53 and 3.</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 353, we need to group it as 53 and 3.</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 3. We can say n is ‘1’ because 1 × 1 = 1 which is less than or equal to 3. Now the<a>quotient</a>is 1, after subtracting 3-1, the<a>remainder</a>is 2.</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 3. We can say n is ‘1’ because 1 × 1 = 1 which is less than or equal to 3. Now the<a>quotient</a>is 1, after subtracting 3-1, the<a>remainder</a>is 2.</p>
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<p><strong>Step 3:</strong>Now let us bring down 53 which forms the new<a>dividend</a>253. Add the old<a>divisor</a>with the same number 1 + 1 to get 2 which will be our new divisor.</p>
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<p><strong>Step 3:</strong>Now let us bring down 53 which forms the new<a>dividend</a>253. Add the old<a>divisor</a>with the same number 1 + 1 to get 2 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 2n 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 2n 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 2n × n ≤ 253. Let us consider n as 9, now 29 × 9 = 261, which is greater than 253. So we try n as 8, now 28 × 8 = 224.</p>
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<p><strong>Step 5:</strong>The next step is finding 2n × n ≤ 253. Let us consider n as 9, now 29 × 9 = 261, which is greater than 253. So we try n as 8, now 28 × 8 = 224.</p>
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<p><strong>Step 6:</strong>Subtract 253 from 224, the difference is 29, and the quotient is 18.</p>
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<p><strong>Step 6:</strong>Subtract 253 from 224, the difference is 29, and the quotient is 18.</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 zeros to the dividend. Now the new dividend is 2900.</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 zeros to the dividend. Now the new dividend is 2900.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 189 because 189 × 9 = 1701.</p>
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<p><strong>Step 8:</strong>Now we need to find the new divisor that is 189 because 189 × 9 = 1701.</p>
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<p><strong>Step 9:</strong>Subtracting 1701 from 2900 gives the result 1199.</p>
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<p><strong>Step 9:</strong>Subtracting 1701 from 2900 gives the result 1199.</p>
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<p><strong>Step 10:</strong>Now the quotient is 18.7.</p>
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<p><strong>Step 10:</strong>Now the quotient is 18.7.</p>
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<p><strong>Step 11:</strong>Continue these steps until the desired decimal places are achieved.</p>
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<p><strong>Step 11:</strong>Continue these steps until the desired decimal places are achieved.</p>
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<p>So the square root of √353 ≈ 18.79.</p>
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<p>So the square root of √353 ≈ 18.79.</p>
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