GCSE · Integers, powers & roots

Powers and roots (squares, cubes, square roots and cube roots)Exam-style questions

What squares, cubes and other powers mean and how to work them out by hand; square roots and cube roots as the way back, including the negative square root and the cube root of a negative number; powers of 10; trapping a root between two whole numbers and closing in to one decimal place by trial; powers and roots on a calculator; and how to compare and order them.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
(a) $x^2 = 100$

Write down both values of $x$ .

(1 mark)
(b) Explain why there is no value of $x$ for which $x^2 = -100$

(1 mark)
Level 2 · 2 marksTry it
2
(a) Write down the two consecutive whole numbers that $\sqrt{58}$ lies between.

(1 mark)
(b) Between which two consecutive whole numbers does $\sqrt[3]{20}$ lie?

(1 mark)
Level 2 · 2 marksTry it