Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Rooted Via 10

How many of the numbers shown are greater than 10?

Largest Expression

Which of these five algebraic expressions is largest, given $x$ is between 0 and 1?

Root Estimation

Age 14 to 16 Short Challenge Level:
Without using a calculator, work out which of the following is the best approximation for $$\sqrt{\frac{2001}{10000}}$$

$0.4,$     $0.42,$     $0.45,$     or     $0.47$

This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.