Question

How to find square root and cube root of a number?

Answer 1

♦ BINOMIAL EXPANSION ♦

--> According to Binomial Theorem, for all 'n' > -1, 'n' < 1 :->

$( 1 + x )^n = 1 + nx + \frac{n(n-1)}{2!} x^{2} + \frac{n(n-1)(n-2)}{3!} x^{3} + ... \infty$

Hence, since, { 1/2 , 1/3 } < 1, according to Binomial Theorem :->

$( 1 + x )^ \frac{1}{2} = 1 + \frac{1}{2}x + \frac{\frac{1}{2}(\frac{1}{2}-1)}{2!} x^{2} + \frac{\frac{1}{2}(\frac{1}{2}-1)(\frac{1}{2}-2)}{3!} x^{3} + ... \infty$

And hence, you calculate the approximate value till the desired accuracy is achieved ^_^

Same goes with the cube root  .. 
Hope this helps you ^_^