Question

Write whether on simplification 2√45 + 3√20 / 2√5 gives a rational or an irrational number.

Answer 1

$\textbf{Given:}$

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

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

$=\displaystyle\frac{2(3\sqrt{5})+3(2\sqrt{5})}{2\sqrt{5}}$

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

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

$=\displaystyle\,6,\;\text{is a rational number}$

$\therefore\textbf{On simplification}\;\displaystyle\frac{2\sqrt{45}+3\sqrt{20}}{2\sqrt{5}}$$\;\textbf{gives a rational number}$