### 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 2017

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

Answer: 44 and 45

Squaring numbers to get close to $2017$
$40^2=1600$ too small
$50^2=2500$ too big, so $\sqrt{2017}$ is between $40$ and $50$.

$45^2=2025$, very close but a bit too big
$44^2=1936$, too small, so $\sqrt{2017}$ is between $44$ and $45$.

You can find more short problems, arranged by curriculum topic, in our short problems collection.