Question

show that root 3+5 is irrational ​

Answer 1

Heya !

Correct Question:-

show that root 3+√5 is iirrational, where √5 is irrational

Solution:-

Let us assume that 3+√5 is rational

then, :-

$\implies$ 3+√5 = p/q

$\implies$ √5 = p/q - 3

$\implies$ √5 = p-3q/q

since, √5 is irrational as given in the Ques.

and p-3q/q is rational.

L.H.S ≠ R.H.S

• This is a contradiction.
• Hence, 3+√5 is irrational.