A square mosaic design covers an area of $700{\text{cm}}^2$. The length of its side lies between which two whole numbers of centimetres?

Useful patterns to spot a perfect square (and reject non-squares):

- **Last digit**: a perfect square ends in 0, 1, 4, 5, 6, or 9 — NEVER in 2, 3, 7, or 8. So 142 cannot be a perfect square (ends in 2).
- **Number of zeros at the end**: must be even. 100 is a perfect square $(10^2)$; 1000 is not.
- **Squares of even numbers are even; squares of odd numbers are odd.**
- **Sum of consecutive odd numbers**: 1 + 3 + 5 + … + $(2n-1)=n^2$. Try it: $1+3+5=9=3^2$.

These let you reject many candidates without doing any heavy work.