Robinson Tuition
Grade 2 · Foundation · free GCSE maths worksheet

Square numbers and cube numbers

Squares to 15 x 15, cubes and their roots.

17 original questions, 25 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 an odd square number between 30 and 60.

1 mark
Show answer
49
2

Here is a list of numbers.

9, 16, 27, 36, 50

Write down the cube number.

1 mark
Show answer
27
3

Write down the value of 62

1 mark
Show answer
36
4

Use your calculator to work out √1296

1 mark
Show answer
36
5

Write down the value of √81

1 mark
Show answer
9
6

Work out

  1. 43
  2. 53
2 marks
Show answer
a) 64 b) 125
7

Work out √196

1 mark
Show answer
14
8

Work out the value of 3√64

1 mark
Show answer
4
9

Work out the value of 0.32

1 mark
Show answer
0.09
10

Tom says, "The cube root of 27 is 9 because 27 ÷ 3 = 9."

Explain Tom's mistake and write down the correct cube root of 27.

2 marks
Show answer
Tom divided by 3; the cube root needs 3 × 3 × 3 = 27, so it is 3
11

A cube has a volume of 125 cm3.

  1. Work out the length of one edge of the cube.
  2. Work out the area of one face of the cube.
2 marks
Show answer
a) 5 cm b) 25 cm²
12

Work out

  1. 42 + 33
  2. 72 − 23
2 marks
Show answer
a) 43 b) 41
13

Find the value of √0.64

1 mark
Show answer
0.8
14

Write down the square number that is between 30 and 45

1 mark
Show answer
36
15
  1. Work out (−5)3
  2. Use your calculator to work out √2.56
2 marks
Show answer
a) -125 b) 1.6
16

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)
17

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

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.

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