Estimating Square Roots
• Introduction

In this worksheet, we will practise estimating square roots.

Method

We know the square numbers from 12 to 122
i.e.,  1= 1, 2= 4, 3= 9 etc.

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.

approximately 7.7 (nearer to 8).

• Question 1

Select an approximate value for the following square root.

√104 = _________

8.1

10.2

11.2

9.2

• Question 2

Select an approximate value for the following square root.

√85 = _________

9.2

10.2

5.5

10.8

• Question 3

Select an approximate value for the following square root.

√57 = _________

6.5

7.5

7.1

6.6

• Question 4

Select an approximate value for the following square root.

√123= _________

11.4

12.2

11.1

10.5

• Question 5

Select an approximate value for the following square root.

√15 = _________

3.9

4.5

3.1

3.3

• Question 6

Select an approximate value for the following square root.

√122 = _________

11.1

9.9

11.0

10.9

• Question 7

Select an approximate value for the following square root.

√35 = _________

5.9

6

6.5

5.2

• Question 8

Select an approximate value for the following square root.

√36.1 = _________

5.9

6.0

6.1

5.2

• Question 9

Select an approximate value for the following square root.

√33 = _________

5.2

6

6.5

5.7

• Question 10

Select an approximate value for the following square root.

√92 = _________

9.3

9.6

9.8

9.9

Progress