Given that `sqrt(5)` is irrational, prove that `2sqrt(5)-3` is an irrational number.

Explanation

Let us assume, to the contrary, that `2sqrt(5)-3` is a rational number
`therefore 2sqrt(5)- 3= (p)/(q)` Where p and q are integres and `q ne 0`
` rArr sqrt(5) = (p+3q)/(2q) …….(1)`
Since p and q are integers `therefore (p+3q)/(2q)` is a rational number.
`therefore sqrt(5)` is a rational number which is a contradiction as `sqrt(5)` is an irrational number .
Hence our assumption is wrong and hence `2sqrt(5)-3` is an irrational number.