Question

5+3√2 is irrational s an irrational number prove tha

Answer 1

This is a question from CBSE Maths board exam 2018.
here's the solution...

It is given that √2 is irrational.
We have to prove that 5+3√2 is irrational.

Solution:

Let us assume that 5+3√2 is rational.
Therefore,
5+3√2 = p/q ......(where p & q are integers and q≠0)

√2 = p/3q - 5
here, p/q is rational therefore, p/3q-5 is also rational.
So √2 is also rational as it is equal to p/3q-5.
But, √2 is irrational. (given)

Therefore it contradicts our assumption. 5+3√2 is irrational.

Hence Proved.

hope it helps...