Question

Prove that 3√5-7 is irrational

Answer 1

let 3√​5-7 be rational
3√​5-7+7 here,7is rational
=3√​5 is irrational( this contradict due to wrong assumption)
therefore 3√​5-7 is irrational.

Answer 2

Let us assume to the contrary that 3√5-7 is a rational no.
Such That ,
3√5-7=p/q {where, p and q are integers having no common factors}.
3√5=p/q+7
3√5=.p+7q/q
√5= p+7q/3q
where , √5 and p+7q/3q are rational numbers.


But this contradicts the fact that √5 is irrational.
Therefore,3√5-7 is an irrational no.




MARK AS BRAINLIEST !!