Powers and Roots


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

Sticky Numbers

Stage: 3 Challenge Level: Challenge Level:1

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

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

Generating Triples

Stage: 4 Challenge Level: Challenge Level:1

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

Stage: 4 Challenge Level: Challenge Level:1

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

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Stage: 3 and 4

A collection of short Stage 3 and 4 problems on powers and roots.