0 added
0 removed
Original
2026-01-01
Modified
2026-02-28
1
<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>
1
<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>
2
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1033, we need to group it as 33 and 10.</p>
2
<p><strong>Step 1:</strong>To begin with, we need to group the numbers from right to left. In the case of 1033, we need to group it as 33 and 10.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 10. We can say n as ‘3’ because \(3 \times 3 = 9\) is less than or equal to 10. The<a>quotient</a>is 3. After subtracting \(10 - 9\), the<a>remainder</a>is 1.</p>
3
<p><strong>Step 2:</strong>Now we need to find n whose square is<a>less than</a>or equal to 10. We can say n as ‘3’ because \(3 \times 3 = 9\) is less than or equal to 10. The<a>quotient</a>is 3. After subtracting \(10 - 9\), the<a>remainder</a>is 1.</p>
4
<p><strong>Step 3:</strong>Now, bring down 33, which makes the new<a>dividend</a>133. Add the old<a>divisor</a>with the same number: \(3 + 3 = 6\), which will be our new divisor.</p>
4
<p><strong>Step 3:</strong>Now, bring down 33, which makes the new<a>dividend</a>133. Add the old<a>divisor</a>with the same number: \(3 + 3 = 6\), which will be our new divisor.</p>
5
<p><strong>Step 4:</strong>The new divisor will be 6n. Now we need to find the value of n such that \(6n \times n \leq 133\). Let us consider n as 2, now \(62 \times 2 = 124\).<strong></strong></p>
5
<p><strong>Step 4:</strong>The new divisor will be 6n. Now we need to find the value of n such that \(6n \times n \leq 133\). Let us consider n as 2, now \(62 \times 2 = 124\).<strong></strong></p>
6
<p><strong>Step 5:</strong>Subtract \(133 - 124\); the difference is 9, and the quotient is 32.<strong></strong></p>
6
<p><strong>Step 5:</strong>Subtract \(133 - 124\); the difference is 9, and the quotient is 32.<strong></strong></p>
7
<p><strong>Step 6:</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>
7
<p><strong>Step 6:</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>
8
<p><strong>Step 7:</strong>Now we need to find the new divisor that is 644, because \(644 \times 1 = 644\).</p>
8
<p><strong>Step 7:</strong>Now we need to find the new divisor that is 644, because \(644 \times 1 = 644\).</p>
9
<p><strong>Step 8:</strong>Subtracting 644 from 900, we get the result 256.</p>
9
<p><strong>Step 8:</strong>Subtracting 644 from 900, we get the result 256.</p>
10
<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. If there is no remaining value, continue until the remainder is zero.</p>
10
<p><strong>Step 9:</strong>Continue doing these steps until we get two numbers after the decimal point. If there is no remaining value, continue until the remainder is zero.</p>
11
<p>So the square root of √1033 ≈ 32.15598.</p>
11
<p>So the square root of √1033 ≈ 32.15598.</p>
12
12