Question

How do you find a square root of a decimal?

Answer 1

Step 1: Define the method of long division to calculate the square root

1. In order to calculate the square root of a given number, first, group the digits of the number in pairs.
2. Mark the pairs of digits using bar brackets starting from the unit place or right-hand side of the number.
3. In the case of an even number of digits, all the digits will be in pairs.
4. In the case of an odd number of digits, the digit at the extreme left will not form a pair.
5. In the case of decimal numbers, the pair of digits are formed starting from the decimal on either side (left and right).
6. Take the largest number as the divisor whose square is less than or equal to the digit on the extreme left (or the first pair of digits) of the number.
7. Write the same number as the quotient as well.
8. The digit (or the pair of digits) on the extreme left of the given number is the dividend.
9. Square the quotient and write it below the dividend and perform subtraction.
10. Write down the remainder and bring down the next pair of digits beside the remainder. This number will be the new dividend.
11. Double the quotient and write it as a divisor of the new dividend.
12. Now select the largest digit for the unit place of the new divisor such that the new number, when multiplied by the new digit at the unit’s place, is equal to or less than the new dividend.
13. Also, write this digit in the quotient.
14. If the product is equal to the new dividend, then the remainder is zero. And the number written as the quotient is the required square root of the given number.
15. If the remainder is not zero and there are more pairs of digits available in the given number, continue the same procedure.

Step 2: Explain with the help of an example

Let us suppose a decimal number, say, $6.25$.

Applying the long division method to find the square root,

So, $\sqrt{6.25}=2.5$

Hence, the square root of a decimal number can be determined using the long division method.