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Given that √2 is irrational, prove …

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Given that √2 is irrational, prove that (5+3√2) is an irrational

Posted by Kishan Kumar 6 years, 9 months ago

CBSE > Class 10 > Mathematics

2 answers

Anushka S 6 years, 9 months ago

Let 5+3√2 is rational number say p/q where q is not equal to zero and p and q is coprime. 5+3√2=p/q 3√2=p/q-5 3√2=p-5q/q √2=p-5q/3q √2is irrational and p-5q/3q is rational. Therefore our supposition is wrong. 5+3√2 is irrational

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Jaya Maji 6 years, 9 months ago

Let assume √2 as a rational no. It can be wriien as a/b where a,b both r integers so a/b=5+3√2 .now a/b -5=3√2,now a-5b/b= 3√2and a-5b/3b =√2 bt it can't happen bcz a,b both r integers so r.h.s not equals to l.h.s so assumption is wrong and hence it is proved that 5+3√2 is an irrational no.

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