Question

Compare the following surds:
$7\sqrt{2},5\sqrt{3}$

Answer 1

$\frac{7\sqrt{2}}{5\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}}=\frac{7\sqrt{6}}{15}$

As $\sqrt{6}\cong 2.4$

$\Rightarrow 7\times 2.4=16.8>15$

$\Rightarrow 7\sqrt{2}>5\sqrt{3}$.