A lot of the time, when we aren't using a calculator, we can't get exactly correct answers to questions. In these instances, we have to estimate answers.

Estimating means "making an educated guess". This time, we're going to look at how we do this with square numbers and square roots.

Square numbers:

To be able to do this, we must know our square numbers up to 10^{2}. These are 1,4,9,16, 25, 36, 49, 64, 81 and 100

**Example 1: Estimating a square root**

Which two integers does √80 lie?

To do this, we need to look at which square numbers 80 is. We can see it is between 64 and 81.

As √64 = 8 and √81 = 9, √80 must be between 8 and 9 (as 80 is closer to 81 than 64, √80 will be very close to 9)

**Example 2: Estimating a square number**

Which two squares will 7.1^{2} lie?

Again, we need to look at our square numbers. 7.1 is between 7 and 8

With 7^{2} = 49 and 8^{2} = 64

Therefore, 7.1^{2} must be between 49 and 64