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  1. Maths
  2. Year 8
  3. Powers and Roots
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Estimating Square Roots

In this worksheet, students practise estimating square roots.

'Estimating Square Roots' worksheet

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Understand Integer Powers/Real Roots

Difficulty level:  

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Worksheet Overview

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.,  12 = 1, 22 = 4, 32 = 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

  • ANSWERS
  • Question 1

Select an approximate value for the following square root.

 

√104 = _________

CORRECT ANSWER
10.2
  • ANSWERS
  • Question 2

Select an approximate value for the following square root.

 

√85 = _________

CORRECT ANSWER
9.2
  • ANSWERS
  • Question 3

Select an approximate value for the following square root.

 

√57 = _________

CORRECT ANSWER
7.5
  • ANSWERS
  • Question 4

Select an approximate value for the following square root.

 

√123= _________

CORRECT ANSWER
11.1
  • ANSWERS
  • Question 5

Select an approximate value for the following square root.

 

√15 = _________

CORRECT ANSWER
3.9
  • ANSWERS
  • Question 6

Select an approximate value for the following square root.

 

√122 = _________

CORRECT ANSWER
11.0
  • ANSWERS
  • Question 7

Select an approximate value for the following square root.

 

√35 = _________

CORRECT ANSWER
5.9
  • ANSWERS
  • Question 8

Select an approximate value for the following square root.

 

√36.1 = _________

CORRECT ANSWER
6.0
  • ANSWERS
  • Question 9

Select an approximate value for the following square root.

 

√33 = _________

CORRECT ANSWER
5.7
  • ANSWERS
  • Question 10

Select an approximate value for the following square root.

 

√92 = _________

CORRECT ANSWER
9.6
---- OR ----

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