Powers and roots

problem
Power countdown

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

How much money did the Queen give away in pence as a power of 2?
problem
Unusual long division - square roots before calculators

Age

14 to 16

Challenge level

However did we manage before calculators? Is there an efficient way to do a square root if you have to do the work yourself?
problem
Negative power

Age

14 to 16

Challenge level

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?
problem
Twelve cubed

Age

14 to 16

Challenge level

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?
problem
Integer indices

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

Age

16 to 18

Challenge level

Investigate powers of numbers of the form (1 + sqrt 2).
problem
Equal temperament

Age

14 to 16

Challenge level

The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.