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Prove that root 3+root 5 is …

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Prove that root 3+root 5 is irrational

Posted by Esha Mathur 6 years, 3 months ago

CBSE > Class 10 > Mathematics

3 answers

Prerna Kumari 6 years, 3 months ago

???

Satyam Jaiswal 6 years, 3 months ago

Let 3+root5 is rational number Now 3+root5=a/b Then root5=a/b_3 Since a/b_3 is a rational number, so root 5 is also a rational number, but contradicts with the fact that root 5 is irrational, 3+root 5 is irrational number

Gaurav Seth 6 years, 3 months ago

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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