Question

Prove that root 3 +root5 is irrational​

Answer 1

let√3+√5is a rational no.
√3+√5=p/q
√3=p/q-√5
rhs is not equal to lhs because a irrstional no. is not equal to a ratinsl no
our assption is wrong
it is an irrational no.
hence proved

Answer 2

Hello friend

Here's your answer

To prove: √3+√5 is irrational

To prove it let us assume it to be a rational number

Rational numbers are the ones which can be expressed in p/q form where p,q are integers and q isn't equal to 0

√3+√5=p/q

√3=(p/q)-√5

Squatting on both sides

3=p²/q²-(2√5p)/q+5

(2√5p)/q=5-3-p²/q²

2√5p/q=(2q²-p²)/q²

√5=(2q²-p²)/q²*q/2p

√5=(2q²-p²)/2pq

As p and q are integers RHS is rational

As RHS is rational LHS is also rational i.e √5 is rational

But this contradicts the fact that √5 is irrational

This contradiction arose because of our false assumption

So √3+√5 is irrational.