Question

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Answer 1

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LET √3+√5 IS AN RATIONAL NO.
HENCE,
√3+√5=P/Q WHERE Q IS NOT EQUAL YO ZERO.

√3+√5=P/Q
√3=P/Q-√5
THEN SQUARING ON BOTH SIDES
3=P²/Q²-5
THEN TAKE L.C.M
3=P²-5Q²/Q
IT IS RATIONAL NO.
HENCE √3+√5 IS IRRATIONAL NO.
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Answer 2

★ HERE IS 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.

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