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Our online tools will provide quick answers to your calculation and conversion needs. On this page, you can find square root of a number using division method with step by step instructions.

Enter positive whole number or decimal

Result window

Sample: Square root of 5 using division method

Group the digits into pairs (For digits to the left of the decimal point, pair them from right to left. For digits after decimal point, pair them from left to right).
Thus we have, 05

Perform division as per steps shown below:

1.

Find the largest number whose square is less than or equal to the number in the leftmost group (22 < 5 < 33). Take this number as the divisor and the quotient with the number in the leftmost group as the dividend (05). Divide and get the remainder (1 in this case).

2
205
4
1

2. Put the decimal point.

3.

Remember: A decimal number, say, 3 can be written as 3.0, 3.00 and so on. Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 42 × 2 = 84, so we choose the new digit as 2. Get the remainder.

2.2
205.00
+24
42100
84
16

4.

Remember: A decimal number, say, 3 can be written as 3.0, 3.00 and so on. Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 443 × 3 = 1329, so we choose the new digit as 3. Get the remainder.

2.23
205.0000
+24
42100
+284
4431600
1329
271

5.

Remember: A decimal number, say, 3 can be written as 3.0, 3.00 and so on. Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 4466 × 6 = 26796, so we choose the new digit as 6. Get the remainder.

2.236
205.000000
+24
42100
+284
4431600
+31329
446627100
26796
304

End of long division (upto 3 decimal places).

√5 = 2.236

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