Powers and roots

  • eNRICHing experience
    problem

    eNRICHing Experience

    Age
    14 to 16
    Challenge level
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    Find the five distinct digits N, R, I, C and H in the following nomogram

  • Powers of Four
    problem

    Powers of Four

    Age
    14 to 16
    Challenge level
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    Can you work out the value of x in this 'power-full' equation?

  • Twelve Cubed
    problem

    Twelve Cubed

    Age
    14 to 16
    Challenge level
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    A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?

  • Rationals Between...
    problem

    Rationals Between...

    Age
    14 to 16
    Challenge level
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    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?

  • Near 10
    problem

    Near 10

    Age
    14 to 16
    Challenge level
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    10 must remain within easy reach...

  • Powerful Order
    problem

    Powerful Order

    Age
    14 to 16
    Challenge level
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    Powers of numbers might look large, but which of these is the largest...

  • 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?

  • Integer Indices
    problem

    Integer Indices

    Age
    14 to 16
    Challenge level
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    From this sum of powers, can you find the sum of the indices?