Cube Root by Approximation Method

Cube Root by Approximation Method

The cube root of a number always push us in back seat as there is no proper method to find the cube root of a number which is not a perfect cube. But the method I am discussing here will surely bring a smile on your face and you will love it.

Approximation method: -

Cube root of a number less than 1000 which is not a cubic number can be extracted by this formula. This rule is called Approximation method and many of you who have read Calculus might have done this question. The best part of this method is that you can do calculation in seconds if you have learnt the cube of first ten natural numbers.

Cube root to be extracted = 

                         Nearest perfect cubic number ±       Deviation                                                                                                                                               3 × (Square of Perfect cubic number) 

Example: - Find the cube root of 128

Solution: - Nearest cubic number of 128 is 125 whose cube root is 5.                                                                       

Deviation = 128 – 125 = 3

Hence, (128)¹/₃ = 5 + 3/ 3 × 5²           

                   = 5 + 0.04 = 5.04              

                                                                                                

Example: - Find the cube root of 761

Solution: - Nearest cubic number of 761 is 729 whose cube root is 9.                                                                       

Deviation = 761 – 729 = 32

Hence, (761)¹/₃ = 9 + 32/ 3 × 9²         

                        = 9 + 0.131 = 9.131                                                                                                            

Example: - Find the cube root of 214

Solution: - Nearest cubic number of 214 is 216 whose cube root is 6.                                                                       

Deviation = 214 – 216 = −2

Hence, (214)¹/₃ = 6 − 2/ 3 × 6² 

          = 6 − 0.018 = 5.982                                                                                                           

This method will give you approximate result so you can’t compare it with the calculator result. But the fact of the matter is that this is correct up to at least 2 decimal places and this serves our purpose.

I hope you have learnt the method of extracting cube root of any number whether it is a perfect cube or not through short cut method which will be immense help in competitive examination where speed play a vital role.

 ^{Are you enjoying the method discussed in my blog?}

What are you waiting for --

Send your valuable comments to me. Don't forget to read my book Maths Made Easy published by Rupa Publication and available on all major websites like - amazon, snapdeal, flipkart ---- etc. 

Rajesh Kumar Thakur

rkthakur1974@gmail.com

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