Robinson Tuition
Grade 3 · Foundation · free GCSE maths worksheet

Powers and roots

Squares, cubes, square roots and cube roots.

21 original questions, 32 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Write down the value of 62

1 mark
Show answer
36
2

Use your calculator to work out √1296

1 mark
Show answer
36
3

Work out the cube of 3.

1 mark
Show answer
27
4

Write down the value of √81

1 mark
Show answer
9
5

Use your calculator to work out 2.54

1 mark
Show answer
39.0625
6

Work out the value of 25

1 mark
Show answer
32
7

Work out the value of 3√64

1 mark
Show answer
4
8

Work out the value of 0.32

1 mark
Show answer
0.09
9

Find the value of √0.64

1 mark
Show answer
0.8
10

Here are six numbers.

9   15   25   27   30   50

  1. Write down the cube number.
  2. Write down two square numbers.
3 marks
Show answer
a) 27 b) 9 and 25
11

Work out √36 + 42

2 marks
Show answer
22
12

Use your calculator to work out the value of 4.63

1 mark
Show answer
97.336
13

Here are five numbers.

6   9   16   27   40

Write down the two numbers that are powers of 3

1 mark
Show answer
9 and 27
14

Write down the square number that is between 30 and 45

1 mark
Show answer
36
15

Work out 53 − √121

2 marks
Show answer
114
16

Use your calculator to work out 3√1.728

2 marks
Show answer
1.2
17
  1. Work out (−5)3
  2. Use your calculator to work out √2.56
2 marks
Show answer
a) -125 b) 1.6
18

Liam says,

"When you square a number, the answer is always bigger than the number you started with."

Give an example to show that Liam is wrong.

2 marks
Show answer
Any counter-example, e.g. 0.5² = 0.25, which is smaller than 0.5 (or 1² = 1, or 0² = 0)
19

Aisha says,

"32 can be written as the sum of two square numbers."

Is Aisha correct?

You must show your working.

3 marks
Show answer
Yes, Aisha is correct: 32 = 16 + 16 = 4² + 4²
20

Write 2 × 2 × 2 × 5 × 5 using powers.

2 marks
Show answer
23 x 52
21

√200 lies between two whole numbers.

Write down the two whole numbers.

2 marks
Show answer
14 and 15

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

All Grade 3 topics