Question

What is the square root of 201.

Answer 1

Approx. 14.16

Explanation:

First note that sqrt(196) = 14 and that the next higher perfect square is 225, whose sqrt is 15. Thus,

sqrt(201) is in between 14 and 15.

You could use an approach called "extrapolation" to approximate the root of 201:

The difference between 225 and 196 is 31; the difference between 201 and 196 is 5. So, form the proportion (5/31) and add this to 14:

Approx. root of 201 is 14 + (5/31), approximately, or 14.16.

Note that sqrt(201) done on the calculator is 14.18, which is better than 14.16, but these two results are nevertheless quite close.

Answer 2

14.17 (or 14.1744688)