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.

Start practising Read the lesson

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

DifficultyAllLevel 2Level 3Level 4
  1. 1
    (a) x2=100x^2 = 100

    Write down both values of xx.

    (1 mark)
    (b) Explain why there is no value of xx for which x2=−100x^2 = -100

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

    (1 mark)
    (b) Between which two consecutive whole numbers does 203\sqrt[3]{20} lie?

    (1 mark)
    Level 2 · 2 marksTry it
  3. 3
    nn is a whole number.

    5<n<65 < \sqrt{n} < 6
    (a) Write down the largest possible value of nn.

    (1 mark)
    (b) How many possible values of nn are there?

    (2 marks)
    Level 3 · 3 marksTry it
  4. 4
    Without using the square root key on a calculator, use trials to find 30\sqrt{30} correct to 11 decimal place.

    You must show your working.

    (3 marks)
    Level 3 · 3 marksTry it
  5. 5
    Work out (196−23)2\left(\sqrt{196} - 2^3\right)^2

    (3 marks)
    Level 3 · 3 marksTry it

6 more questions on powers and roots (squares, cubes, square roots and cube roots)

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free