Powers and roots

  • Pocket money
    problem

    Pocket money

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    Which of these pocket money systems would you rather have?

  • Power mad!
    problem

    Power mad!

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

  • Magic potting sheds
    problem

    Magic potting sheds

    Age
    11 to 16
    Challenge level
    filled star filled star empty star

    Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

  • More Magic Potting sheds
    problem

    More magic potting sheds

    Age
    11 to 16
    Challenge level
    filled star filled star filled star
    The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
  • Power Countdown
    problem

    Power countdown

    Age
    14 to 16
    Challenge level
    filled star empty star empty star

    In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

  • Double Trouble
    problem

    Double trouble

    Age
    14 to 16
    Challenge level
    filled star empty star empty star

    Simple additions can lead to intriguing results...

  • Rationals Between...
    problem

    Rationals between...

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    What fractions can you find between the square roots of 65 and 67?
  • Archimedes and numerical roots
    problem

    Archimedes and numerical roots

    Age
    14 to 16
    Challenge level
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    The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
  • Number rules - OK
    problem

    Number rules - OK

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Can you produce convincing arguments that a selection of statements about numbers are true?

  • Perfectly Square
    problem

    Perfectly square

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    The sums of the squares of three related numbers is also a perfect square - can you explain why?