Square Roots of Decimals
Consider the problem:
Find the value of:
- Like in the earlier cases: Place the bars over every pair of digits starting from the one’s digit which gives us(17 .64)
- Finding the square which is less than or equal to 17, we get:
< 17. - Here,
becomes the first digit of the quotient and we get a remainder of when subtracting 4 2 - We encounter the decimal in the dividend, so we add in a decimal point in the quotient as well and continue the same process as before.
- Bringing down the number under the next bar (i.e. 64) to the right of the remainder. We now get the new dividend i.e.
- In the divisor put the first digit as double the quotient and place a blank its right. i.e. 8_
- We find that: 82 ×
= 164 - Since, the remainder is
and there are no more digits left in the given number, we get: 17.64 . - We have found the square root of 17.64.
This process can be used to find the square roots of decimal numbers.
Example 13: Find the square root of 12.25
- Like in the earlier cases: Place the bars over every pair of digits starting from the one’s digit which gives us(12 .25)
- Finding the square which is less than or equal to 12, we get:
< 12. - Here,
becomes the first digit of the quotient and we get a remainder of when subtracting 3 2 - We encounter the decimal in the dividend, so we add in a decimal point in the quotient.
- Bringing down the number under the next bar (i.e. 25) to the right of the remainder. We now get the new dividend i.e.
- In the divisor put the first digit as double the quotient and place a blank its right. i.e. 6_
- We find that: 65 ×
= 325 - Since, the remainder is
and there are no more digits left in the given number, we get: 12.25 . - We have found the square root for the number: 12.25.
Which way to move
Consider a number 176.341. We need to put bars on both the integral part and decimal part. In what way is putting bars on decimal part different from integral part?
For '176': we start from the unit’s place left of the decimal and move towards
For '.341', we start from the decimal and move towards right. This gives us the first bar over
Example 14: Area of a square plot is 2304
Example 15: There are 2401 students in a school. P.T. teacher wants them to stand in rows and columns such that the number of rows is equal to the number of columns. Find the number of rows.
- Say, let the number of rows/columns = x. We know that
x 2 . - To find the value of x, we need to find the
of 2401. - Place a bar over every pair of digits starting from the one’s digit. (24 01)
- From the left, find the square which is less than or equal to the digit. Here we have, (
4 2 5 2 becomes the first digit of the quotient and we get a remainder of when subtracting 4 2 - Bring down the number under the next bar (i.e. 01) to the right of the remainder. We now get the new dividend i.e.
. - In the divisor put the first digit as double the quotient and place a blank its right. i.e. 8_
- Put the 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.
- We get that: 89 ×
= 801 - Since, the remainder is
and there are no more digits left in the given number, we get: 2401 . - We have found the square root of 2401.