Question

show that 7 -3root 7 is irrational no..

Answer 1

let assume 7-3√7 be a rational no.
7-3√7=r...... (say)
-3√7=r-7
$\sqrt{7} = \frac{r - 7}{ - 3}$
r is a rational no
=> r-7 is a rational no
$\frac{r - 7}{ - 3} \: is \: also \: a \: rational \: no.$
=> RHS is a rational no.
=> LHS is also a rational no
but √7 is an irrational no
=> Our assumption is wrong.
=>7-3√7 is an irrational no.