### 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:

We can try squaring numbers to get close to $2017$.

$4^2=16$ and $5^2=25$, so $40^2=1600$ and $50^2=2500$, so $\sqrt{2017}$ is between $40$ and $50$.

$45^2=2025$, which is very close to $2017$ but a bit larger, so $\sqrt{2017}$ must be between $44$ and $45$.

(You can check that $44^2=1936<2017$)
You can find more short problems, arranged by curriculum topic, in our short problems collection.