Powers and Roots

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Sticky Numbers

Age 11 to 14 Challenge Level:

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Sissa's Reward

Age 11 to 14 Challenge Level:

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

Generating Triples

Age 14 to 16 Challenge Level:

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

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.

A Question of Scale

Age 14 to 16 Challenge Level:

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Powers and Roots - Short Problems

Age 11 to 16

A collection of short problems on powers and roots.

Pocket Money

Age 11 to 14 Challenge Level:

Which of these pocket money systems would you rather have?

You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.