Powers and roots

  • Irrational arithmagons
    problem

    Irrational arithmagons

    Age
    16 to 18
    Challenge level
    filled star filled star empty star

    Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?

  • Cube Roots
    problem

    Cube roots

    Age
    16 to 18
    Challenge level
    filled star filled star filled star
    Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.
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