# Estimating Square Roots

In this worksheet, students practise estimating square roots.

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Understand Integer Powers/Real Roots

Difficulty level:

### QUESTION 1 of 10

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).

Select an approximate value for the following square root.

√104 = _________

8.1

10.2

11.2

9.2

Select an approximate value for the following square root.

√85 = _________

9.2

10.2

5.5

10.8

Select an approximate value for the following square root.

√57 = _________

6.5

7.5

7.1

6.6

Select an approximate value for the following square root.

√123= _________

11.4

12.2

11.1

10.5

Select an approximate value for the following square root.

√15 = _________

3.9

4.5

3.1

3.3

Select an approximate value for the following square root.

√122 = _________

11.1

9.9

11.0

10.9

Select an approximate value for the following square root.

√35 = _________

5.9

6

6.5

5.2

Select an approximate value for the following square root.

√36.1 = _________

5.9

6.0

6.1

5.2

Select an approximate value for the following square root.

√33 = _________

5.2

6

6.5

5.7

Select an approximate value for the following square root.

√92 = _________

9.3

9.6

9.8

9.9

• Question 1

Select an approximate value for the following square root.

√104 = _________

10.2
• Question 2

Select an approximate value for the following square root.

√85 = _________

9.2
• Question 3

Select an approximate value for the following square root.

√57 = _________

7.5
• Question 4

Select an approximate value for the following square root.

√123= _________

11.1
• Question 5

Select an approximate value for the following square root.

√15 = _________

3.9
• Question 6

Select an approximate value for the following square root.

√122 = _________

11.0
• Question 7

Select an approximate value for the following square root.

√35 = _________

5.9
• Question 8

Select an approximate value for the following square root.

√36.1 = _________

6.0
• Question 9

Select an approximate value for the following square root.

√33 = _________

5.7
• Question 10

Select an approximate value for the following square root.

√92 = _________

9.6
---- OR ----

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