Question

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

Answer 1

Let us simplify  `(2sqrt45 +3 sqrt20)/(2sqrt5)`

`(2sqrt45+3sqrt20)/(2sqrt5)=(6sqrt5+6sqrt5)/(2sqrt5)`

`=(12sqrt5)/(2sqrt5)`

`=6`

6 is rational number