Question

given the √2 is irrational number, prove (5+3√2) is an irrational number

Answer 1

Let us assume that 5+3√2 is rational...

5+3√2 = a/b
3√2 = a/b - 5
3√2 = a-5b/b
√2 = a-5b/3b

But as we know that √2 is irrational number..

√2 is not equal to a-5b/3b

Hence , 5+3√2 is irrational number!!

Hope this helps!!
cheers!! (:

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