Powers and roots

  • Small tomato seedlings in pink pots.
    problem

    Powers of Four

    Age
    14 to 16
    Challenge level
    1 out of 3

    Can you work out the value of x in this 'power-full' equation?

  • Small pepper seedlings in turquoise pots.
    problem

    Twelve Cubed

    Age
    14 to 16
    Challenge level
    1 out of 3

    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
    2 out of 3

    What fractions can you find between the square roots of 65 and 67?

  • Consecutive Squares
    problem

    Consecutive Squares

    Age
    14 to 16
    Challenge level
    2 out of 3

    The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

  • Archimedes and numerical roots
    problem

    Archimedes and Numerical Roots

    Age
    14 to 16
    Challenge level
    2 out of 3

    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?

  • Small pepper seedlings in orange pots.
    problem

    Near 10

    Age
    14 to 16
    Challenge level
    2 out of 3

    10 must remain within easy reach...

  • Small tomato seedlings in pink pots.
    problem

    Powerful Order

    Age
    14 to 16
    Challenge level
    2 out of 3

    Powers of numbers might look large, but which of these is the largest...

  • Small tomato seedlings in pink pots.
    problem

    Roots Near 9

    Age
    14 to 16
    Challenge level
    2 out of 3

    For how many integers n is the difference between √n and 9 less than 1?

  • Small tomato seedlings in pink pots.
    problem

    Integer Indices

    Age
    14 to 16
    Challenge level
    3 out of 3

    From this sum of powers, can you find the sum of the indices?