# How To Solve Square Roots

## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

#### SIGN UP FOR A FREE TRIAL

If the index of a positive number x is half √x then it is known as square root of x.

How to solve square roots: -

Question 1: - Find the square root of 384 (or √384)

 Steps Solution Step 1: - Try to factorize a 384 to their possible smallest value. 384 can be written as 384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 Step 2: - Choose the pair of numbers. There are three pairs of 2 and the remaining 2 unpaired numbers are 2 and 3 like, (2 x 2) x (2 x 2) x (2 x 2) x (2 x 3) Step 3: - Take out the pair of a number as a single number. 3 pair of 2 will come outside the square root and will be written as a single number. 2 x 2 x 2 x √ ( 2 x 3) Step4: - Multiply the numbers which is outside and inside the square root separately. √384 = 8 √6 (since 2x2x2 =8 and 2 x 3 = 6)

Therefore √384 = 8 √6

Question 2: - Simplify √27

Solution: -
√ 27 = √ (3 x 3 x 3) = 3 √3

Therefore, 27 = 3 √3.

Question 3: - Simplify √64

Solution: -
√64 = √ (2 x 2 x 2 x 2 x 2 x 2) = 2 x 2 x 2 = 8
Therefore √ 64 = 8