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Prove that underroot 5 irrational no …

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Prove that underroot 5 irrational no by contradiction method

Posted by Satinderpal Ghuman 6 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Khushboo Giri 6 years, 10 months ago

Let √5 be a rational number say,p/q where q is not equal to zero and p&q are co prime. √5=p/q Squaring both side 5=p²/q² 5q²=p²--------------(1) 5q² is divisible by 5 q²is divisible by 5 q is divisible by 5 Let q=5a Putting the value in (1) 5q²=(5a)² 5q²=25a² q²=5a² 5a² is divisible by 5 q²is divisible by 5 q is divisible by 5 p&q has common factor 5 But we assumed they are co prime. It's a contradiction. Our supposition is wrong. Therefore √5 is irrational.

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