CLASS-7
FINDING SQUARE ROOT OF DECIMAL NUMBERS

FINDING SQUARE ROOT OF DECIMAL NUMBERS -

Finding the square root of a decimal number using the long division method follows a similar process as for whole numbers, with extra steps for handling decimal points.

Let's go through it step by step.

Steps to Find the Square Root of a Decimal Using the Long Division Method.

Example.1) Find the square root of 12.25

Ans.)

Step 1:- Pair the Digits

Place a bar over pairs of digits starting from the decimal point.
For 12.25, pair the digits as (12) . (25)

Step 2:- Find the Largest Square

Find the largest number whose square is ≤ 12.
3 × 3 = 9 (fits because 4 × 4 = 16, which is too large).
Write 3 in the quotient.
Subtract 9 from 12, leaving 3.
Bring down the next pair 25 (making it 325).

Step 3:- Double the Quotient

Double 3 (the quotient so far) → 6.
Now we need to find a digit X such that (6X) × X is close to 325.
Trying 65 × 5 = 325, which fits exactly.
Place 5 in the quotient.

Step 4:- Answer

The quotient is 3.5.
Thus, √12.25 = 3.5. (Ans.)

Key Points for Decimals:-

If the number has an odd number of decimal places, add a zero at the end before pairing.
If more precision is needed, continue the process by adding pairs of zeros.
This method works for all decimal numbers!

Example.2) Find the square root of decimal 12.0409

Ans.) Steps:-

1. Starting from decimal point, put arrows or bars on pairs of integers from right to left (←) as usual and on the decimals part from left ti right (→).

Example.3) Find the square root of decimal 0.00064516

Ans.) Steps:-

When the square root of a number is not exact, to find its approximate value correct to a certain place of decimal, we obtain the square root of the given number to one more place and then round off to the desired place.

Example.4) Find the square root of 9.81 correct to 2 decimal places.

Ans.)