Powers and roots

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

Simple additions can lead to intriguing results...

Can you produce convincing arguments that a selection of statements about numbers are true?

The sums of the squares of three related numbers is also a perfect square - can you explain why?

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

Explore the relationships between different paper sizes.

Find the sum of this series of surds.

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