Powers and Roots worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 28 marks Sheet 1

2 marks
(a)
Find the value of \(10^2\)

(b)
Find the value of \(9^3\)
3 marks
(a)
Write \(3 \times 3 \times 3 \times 3\) in index form.

(b)
Find the value of \(2^3\)
3 marks
(a)
Work out \(\sqrt{ 81 }\)

(b)
Work out \(\sqrt[3]{ 512 }\)

(c)
Work out \(\sqrt{ 81 } \times \sqrt[3]{ 512 }\)
3 marks
Find the value of \(\sqrt{ 144 } + 7^2 \times 4\)
4 marks
(a)
A square has an area of \(81\) cm\(^2\).

Find the length of one side.

(b)
A cube has a volume of \(27\) cm\(^3\).

Find the length of one edge.
2 marks
Write down the two consecutive whole numbers that \(\sqrt{ 96 }\) lies between.
2 marks
(a)
Find the value of \(12^2\)

(b)
Find the value of \(7^3\)
3 marks
(a)
Write \(7 \times 7 \times 7 \times 7\) in index form.

(b)
Calculate the value of \(6^3\)
3 marks
(a)
Work out \(\sqrt{ 100 }\)

(b)
Work out \(\sqrt[3]{ 8 }\)

(c)
Work out \(\sqrt{ 100 } \times \sqrt[3]{ 8 }\)
3 marks
Find the value of \(\sqrt{ 100 } + 3^2 \times 4\)

Answers

(a) \(100\)
(b) \(729\)
(a) \(3^4\)
(b) \(8\)
(a) \(9\)
(b) \(8\)
(c) \(72\)
\(208\)
(a) \(9\ \text{cm}\)
(b) \(3\ \text{cm}\)
\(9\) and \(10\)
(a) \(144\)
(b) \(343\)
(a) \(7^4\)
(b) \(216\)
(a) \(10\)
(b) \(2\)
(c) \(20\)
\(46\)