Estimate Powers and Roots

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 10².

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 7.1² lie?

Again, we need to look at our square numbers.

7.1 is between 7 and 8.

7² = 49, 8² = 64

Therefore, 7.1² 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.