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Given that Root 5 is irrational …

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Given that Root 5 is irrational ,prove that 2root 5-3 is an irrational no.

Posted by Ritu Tomar 5 years, 8 months ago

CBSE > Class 10 > Mathematics

1 answers

Tanu Kumari 5 years, 8 months ago

Let us assume on the contrary that 2√5-3 is rational. Then,there exist co-prime integer a and b such that 2√5-3=a/b 2√5=a/b+3 √5=1/2(a/b-3) ( that is a,b are integer,therefore 1/2 (a/b -3) is a rational no.) We know that, √5 is an irrational no. (given) This is contradicts the fact that √5 is irrational.So, our assumption is incorrect.Hence ,2√5 -3 us an irrational number. ??

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CBSE > Class 10 > Mathematics