The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Estimating Square and Cube Roots

In this worksheet, students estimate square roots and cube roots.

'Estimating Square and Cube Roots' worksheet

Key stage:  KS 3

Curriculum topic:  Number

Curriculum subtopic:  Understand Integer Powers/Real Roots

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

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.

 

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

 

1 2 3 4 5 6 7 8 9 10
1 8 27 64 125 216 343 512 729 1000

 

This means that the 3√729 = 9 and 3√1000 = 10.

It also means that the cube root of any number between 729 and 1000 lies between 9 and 10.

Between which two numbers does the following square root lie?

 

√10

3 and 4

2 and 3

7 and 8

Between which two numbers does the following square root lie?

 

√30

5 and 6

2 and 3

3 and 4

Between which two numbers does the following cube root lie?

 

3√62

7 and 8

2 and 3

3 and 4

Between which two numbers does the following square root lie?

 

√50

7 and 8

2 and 3

3 and 4

Between which two numbers does the following cube root lie?

 

3√50

3 and 4

6 and 7

7 and 8

Between which two numbers does the following square root lie?

 

√40

5 and 6

6 and 7

7 and 8

Between which two numbers does the following cube root lie?

 

3√420

5 and 6

6 and 7

7 and 8

Between which two numbers does the following cube root lie?

 

3√999

7 and 8

8 and 9

9 and 10

Between which two numbers does the following square root lie?

 

√65

4 and 5

8 and 9

9 and 10

Between which two numbers does the following cube root lie?

 

3√65

4 and 5

8 and 9

9 and 10

  • Question 1

Between which two numbers does the following square root lie?

 

√10

CORRECT ANSWER
3 and 4
EDDIE SAYS
√10 is between √9 and √16 √10 must be between 3 and 4
  • Question 2

Between which two numbers does the following square root lie?

 

√30

CORRECT ANSWER
5 and 6
EDDIE SAYS
√30 is between √25 and √36 √30 must be between 5 and 6
  • Question 3

Between which two numbers does the following cube root lie?

 

3√62

CORRECT ANSWER
3 and 4
EDDIE SAYS
3√62 is between 3√27 and 3√64 3√62 must be between 3 and 4
  • Question 4

Between which two numbers does the following square root lie?

 

√50

CORRECT ANSWER
7 and 8
EDDIE SAYS
√50 is between √49 and √64 √50 must be between 7 and 8
  • Question 5

Between which two numbers does the following cube root lie?

 

3√50

CORRECT ANSWER
3 and 4
EDDIE SAYS
3√50 is between 3√27 and 3√64 3√50 must be between 3 and 4
  • Question 6

Between which two numbers does the following square root lie?

 

√40

CORRECT ANSWER
6 and 7
EDDIE SAYS
√40 is between √36 and √49 √40 must be between 6 and 7
  • Question 7

Between which two numbers does the following cube root lie?

 

3√420

CORRECT ANSWER
7 and 8
EDDIE SAYS
3√420 is between 3√343 and 3√512 3√420 must be between 7 and 8
  • Question 8

Between which two numbers does the following cube root lie?

 

3√999

CORRECT ANSWER
9 and 10
EDDIE SAYS
3√999 is between 3√729 and 1000√64 3√999 must be between 9 and 10
  • Question 9

Between which two numbers does the following square root lie?

 

√65

CORRECT ANSWER
8 and 9
EDDIE SAYS
√65 is between √64 and √81 √65 must be between 8 and 9
  • Question 10

Between which two numbers does the following cube root lie?

 

3√65

CORRECT ANSWER
4 and 5
EDDIE SAYS
3√65 is between 3√64 and 3√125 3√65 must be between 4 and 5
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial

Start your trial for £1