### 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.

### Largest Expression

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

### Powers of Four

Can you work out the value of x in this 'power-full' equation?

# Rooted Via 10

##### Age 14 to 16 Short Challenge Level:

Which of the numbers $3\sqrt{11}, 4\sqrt{7}, 5\sqrt{5}, 6\sqrt{3}, 7\sqrt{2}$ are greater than $10$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.