Question

Given that under root 2 is irrational. Prove that 5+3root2 is an irrational

Answer 1

Heya !!

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Given that, √2 is rational.

Let 5+3√2 be irrational.

5+3√2 = a/b, where a and b are integers and (b≠0)

=> 3√2 = (a/b) – 5

=> √2 = (a–5b) / 3b

Therefore (a–5b) / 3b is irrational as √2 is irrational.

But this contradiction has arisen because of our incorrect consumption.

So, we conclude that 5+3√2 is irrational number.

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Hope my ans.'s satisfactory.☺

Answer 2

here your answer
we can assume the given no. as rational and use contradiction method to solve it

HOPE IT WILL HELP YOU