I need to find square root of 71 i think the answer is 71 but i need steps to figure it out

Answer 1

I will ignore your very sloppy English grammar and answer our question...but my answer will NOT be a sloppy as your question.

Remember sqrt(71) is irrational and cannot be represented exactly as a fraction; however, the following will get you successively closer values.

8² = 64 and 9² = 81, i.e. your answer lies between 8 and 9.

There are several ways of getting the answer. Probably the easiest to explain is Newton's method.

x_{1 = (1/2)[9+(71/9)]...if you convert his to a decimal you will have the first 2 figures correct; as a fraction it is 76/9.}

x₂=(1/2)[x₁+(71/x₁)] = 11527/1368 which already has 5 significant figures if converted to a decimal.

By calculator the answer is 8.42615.

P.S. The general form of Newton's method (which, I think is still the way computers/calculators do it) is

x_n+1 = (1/2)[x_n + (N/x_n)] ... and you should expect the number of significant figures to double at each iteration.

There are other methods for extracting square root...but they are more difficult to explain using this editor. The derivation of Newton's method requires calculus to explain (although there may be other ways to explain it).