How to calculate the square root of a number which us not a perfect square?

1. Evaluate √2 correct up to two places of decimal.

Solution:

Using the division method, we may find the value of √2; 
 

 

Therefore, √2 = 1.414     ⇒     √2 = 1.41 (correct tip to 2 places of decimal) 
If we have to find the square root of a number up to ‘n’ places of decimals, the number of digits in the decimal part must be 2n. If they are less than 2n, then affix suitable number of zeros to the extreme right of the decimal part. 

Find the square root of decimal number using long division method. 

But if we have to find the square root of number correct up to ‘n’ places of decimal, then find the square root of number up to (n + 1) places of decimal. 

If the digit at the (n + 1) decimal place is equal to 5 or greater than 5, then the digit at ‘n’ place increases by 1. 

If the digit at (n + 1) decimal place is less than 5, then the digit at ‘n’ place remains the same and deletes the digit at (n + 1) place. 

This is how we find the square root correct up to n decimal places.