Describe how you would estimate the square root of a number that is not a perfect square without using a calculator?

Question

I don't know the answer( honestly) I need help please. Thank you!

Answer 1

The number N that is not a perfect square lies between two perfect squares K² and (K+1)² so choose Z = K + ½ as the estimate.

 

Square it. If it's less than N, select a slightly larger Z as the estimate and repeat this step. If it's more than N, choose a slightly smaller Z as the estimate and repeat this step. Quit when you're satisfied that Z is approximately the square root of N.

 

Example: Square root of 11...lies between 9 & 16 so K² = 9, K = 3, Z = 3.5

Z squared is 12.5 so Z was too big... choose Z = 3.3

 

Z squared is 10.89 which is smaller than N = 11 so now adjust Z upward from 3.3 to 3.4.

 

Z squared is 3.4² = 11.56, too big, adjust Z downward to 3.35

 

3.35² = 11.2225, too big, adjust downward to 3.32; this squared is 11.0224; adjust downward again to 3.315;

Z² = 10.989225  and this is a pretty good estimate for √11.

 

Kind of makes you appreciate the calculator, doesn't it!