Square root of Irrational in few second

                                                       Square root of Irrational

Many a times while solving a problem in Mensuration you might have encountered a situation where you need to find the square root of irrational up to 2 decimal places. Does such situation annoy you? 

Be ready to bring a big smile over your face because once you complete reading this article you will find yourself at an ease.

Square root of Irrational Number =

                      Nearest Perfect square root + Deviation from Irrational number

                                                                   2 x     Nearest Perfect square root

Let us take few examples to understand the modus operandi of extracting the square root of a number that is not a perfect square.

Example: Find the square root of 47

Solution: - Perfect square approaching 47 is 49. Square root of 49 = 7

              Deviation = 47 – 49 = - 2

                 (   47 )^1/2      =     7   −  2

                                                       2 x  7  

                              = 7 – ¹ / 7   = 7 – 0.14 = 6.86

Example : Find the square root of 174

Solution: - Perfect square approaching 174 is 169 and square root of 169 is 13.

                 Deviation = 174 − 169 =5                 

     174    =     13    +  5

                                            2 x  13

               = 13 +  ⁵ / ₂₆

                     = 13. 192

I hope you have enjoyed your journey with square root and you will get mastery over it in due course of practice.

 Don't forget to send me your feedback at

Rajesh Kumar Thakur

rkthakur1974@gmail.com