Powers and roots

  • Place value, integers, ordering and rounding - Short Problems
    problem

    Roots near 9

    Age
    14 to 16
    Challenge level
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    For how many integers n is the difference between √n and 9 less than 1?

  • Guesswork
    problem

    Guesswork

    Age
    14 to 16
    Challenge level
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    Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

  • Fit for photocopying
    problem

    Fit for photocopying

    Age
    14 to 16
    Challenge level
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    Explore the relationships between different paper sizes.

  • Negative 3 to the power of negative 3.
    problem

    Negative powers

    Age
    14 to 18
    Challenge level
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    What does this number mean? Which order of 1, 2, 3 and 4 makes the highest value? Which makes the lowest?

  • Archimedes Numerical Roots
    problem

    Archimedes numerical roots

    Age
    16 to 18
    Challenge level
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    How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

  • Function Pyramids
    problem

    Function pyramids

    Age
    16 to 18
    Challenge level
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    A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

  • Giants
    problem

    Giants

    Age
    16 to 18
    Challenge level
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    Which is the bigger, 9^10 or 10^9 ? Which is the bigger, 99^100 or 100^99 ?

  • In Between
    problem

    In between

    Age
    16 to 18
    Challenge level
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    Can you find the solution to this algebraic inequality?