Powers and roots

problem
Favourite

Magic Potting Sheds

Age

11 to 16

Challenge level

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?
problem
Favourite

More Magic Potting Sheds

Age

11 to 16

Challenge level

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
problem

eNRICHing Experience

Age

14 to 16

Challenge level

Find the five distinct digits N, R, I, C and H in the following nomogram
problem
Favourite

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
Favourite

Double Trouble

Age

14 to 16

Challenge level

Simple additions can lead to intriguing results...
problem

Rationals Between...

Age

14 to 16

Challenge level

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

Archimedes and Numerical Roots

Age

14 to 16

Challenge level

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?
problem
Favourite

Number Rules - OK

Age

14 to 16

Challenge level

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

Perfectly Square

Age

14 to 16

Challenge level

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

Roots Near 9

Age

14 to 16

Challenge level

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