Question

Write whether $\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}$ on simplification gives a rational or an irrational number.

Answer 1

$\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}$

$=\frac{2\sqrt{9\times 5}+3\sqrt{4\times 5}}{2\sqrt{5}}$

$=\frac{2\times 3\sqrt{5}+3\times 2\sqrt{5}}{2\sqrt{5}}$

$=\frac{6\sqrt{5}+6\sqrt{5}}{2\sqrt{5}}$

$=\frac{12\sqrt{5}}{2\sqrt{5}}$

$=6$

So , it gives a rational number