How do you determine which two numbers a square root is between?

Answer 1

You need to know (or be able to find) perfect squares.

Suppose you want to find two numbers that the square root of 27 is between.

You need to find a number, N, such that N2 < 27 but the square of the next number is bigger ie (N + 1)2 > 27

The nearest perfect squares, on either side of 27 are 25 and 36.

That is, 25 < 27 < 36

Taking square roots,

5 < sqrt(27) < 6

However, it is also true that -6 < sqrt(27) < -5