Question

prove that 3 root 5 minus 7 is an irrational number

Answer 1

Let 3√5 -7 is rational no. we can find coprime a a and b ,(b isn't equal to zero) in such a way that, 3√5-7 =a/b.
3√5=a/b+7. [ HCF (a,b)=1,since a,b are coprime]
3√5=a+7b/b
√5=a+7b/3b


√5=integer + integer×integer/ integer × integer
√5= rational no.[ since a,b,3 and 7 are integers]
This contradicts the fact that √5 is irrational no.
our supposition is wrong that 3√5-7 is a rational no.
so we conclude that 3√5-7 is irrational no.

Answer 2

Hey mate .
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The answer is in the attachment

Hope it helps !!