How To Solve Square Roots

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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



 

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