When we aren't using a calculator, it can be very hard to reach exact correct answers to questions and often this level of detail is not required anyway.

In these instances, we need to **estimate** answers.

Estimating means **making an educated guess**.

In this activity, we're going to look at how we do this with square numbers and square roots, which can often give long and complex answers when calculated.

**Square numbers:**

To be able to estimate with numbers of this type, we must know our square numbers up to 10^{2}.

These are: 1,4,9,16, 25, 36, 49, 64, 81, 100.

**e.g. Estimating a square root**

**Between which two integers does √80 lie?**

To do this, we need to look at which square numbers are closest to 80.

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.

**e.g. Estimating a square number**

**Between which two squares will 7.1 ^{2} lie?**

Again, we need to look at our square numbers.

7.1 is between 7 and 8.

7^{2} = 49, 8^{2} = 64

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

In this activity, we will estimate the answers to squared powers and roots so that we are able to work these out without a calculator.

This will be very useful for your mental maths, speed in solving problems, and checking that your answers are feasible.