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

DifficultyAllLevel 2Level 3Level 4
  1. 1
    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
  2. 2
    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
  3. 3
    Work out (196−23)2\left(\sqrt{196} - 2^3\right)^2

    (3 marks)
    Level 3 · 3 marksTry it
  4. 4
    Here is a question and an incorrect solution.

    Question: Work out 36+64\sqrt{36 + 64}

    Solution: 36+64=36+64=6+8=14\sqrt{36 + 64} = \sqrt{36} + \sqrt{64} = 6 + 8 = 14
    (a) Describe the error made.

    (1 mark)
    (b) Write out a correct solution.

    (2 marks)
    Level 3 · 3 marksTry it