Powers and roots

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

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

How much money did the Queen give away in pence as a power of 2?

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

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

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?

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

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

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

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.