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Given that √2 is irrational, prove that (5+3√2) is an irrational |
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Answer» 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/q3√2=p/q-53√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 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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