1. Square root of Fraction and Decimal

2. Square roots of fraction
Square root of fraction =

3. Example 1 Find the square root of using prime factorization method
Now we find square root of 625 and 256 separately
= 5 x 5 x 5 x 5 = 54
256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2=28
Therefore

4. Example 1 Find the square root using long division method
Now we find square root of 625 and 256 separately
Therefore

5. Square root of Decimal number
To apply the long division method, we write the given number by pairing off the digits as usual in the integral part, and pairing off the digits in the decimal part from left to right after the decimal part.
For Example, we write the number as

6. Example Find the square root of 6.0516
Solution: Step 1: We write the number as Step 2: We can see the number of digits in integral part is 1, so square root will also have 1 digit in integral part. Step 3: We follow the same procedure as long division method to Therefore, square root of is 2.46

7. Try these