The areas of two similar triangles are in the ratio 2 : 3. Find the ratio of their corresponding sides.

Area ratio = $(sideratio{)}^2$, so the side ratio is $\sqrt{\frac{2}{3}}=\frac{\sqrt{2}}{\sqrt{3}},i.e$. √2 : √3. Not every area ratio has a tidy square root. Answering 2 : 3 forgets the square root altogether, 4 : 9 squares when it should have rooted, and 1 : 1.5 is only 2 : 3 rewritten as a decimal.