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Powers and roots – practice for Years 8–9

Sample questions on Powers and roots with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 8–9
Curriculum area
Number and algebra

Question types: Powers and roots

Rule: Powers and roots

a² = a × a, a³ = a × a × a. √a is the number whose square is a: √49 = 7.

The square of a negative number is positive: (−3)² = 9.

Example: √49 × √36 = 7 × 6 = 42

Watch out: 3² = 3 × 3 = 9, not 3 × 2 = 6.

Sample questions

  1. Question 1 Easy

    Work out: (6 − 11)²

    Show the solution
    Answer: 25

    How it works: 6 − 11 = −5; (−5)² = 25

  2. Question 2 Normal

    Work out: 7² + √81

    Show the solution
    Answer: 58

    How it works: 7² = 49, √81 = 9; 49 + 9 = 58

  3. Question 3 Hard

    Work out: √36 × √49

    Show the solution
    Answer: 42

    How it works: √36 = 6, √49 = 7; 6 × 7 = 42

Related topics

All Maths topics

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