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Estimate Square Roots

In this worksheet, students will practise estimating square roots.

'Estimate Square Roots' worksheet

Key stage:  KS 3

Year:  Year 8 Maths worksheets

Curriculum topic:   Number

Curriculum subtopic:   Understand Integer Powers/Real Roots

Popular topics:   Numbers worksheets, Estimation worksheets, Square Numbers worksheets

Difficulty level:  

Worksheet Overview

In this worksheet, we will practise estimating square roots.


This table shows the first few whole numbers and their squares.


1 2 3 4 5 6 7 8 9 10
1 4 9 16 25 36 49 64 81 100


This means that the √81 = 9 and √100 = 10.

It also means that the square root of any number between 81 and 100 lies between 9 and 10.


We can estimate the square roots of numbers between the square numbers.

√7 is between √4 and √9  ie. 2 and 3.

So √7 is approximately 2.6  (7 is nearer to 9 than to 4)

√59 is between √49 and √64 between 7 and 8.

It is nearer to 8, so we could say it is approximately 7.7 


Does that all make sense?


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