Given that √2 is irrational, prove that (5 + 3 √2) is an irrational number. (CBSE 2018)

We will prove this statement by contradiction.

Let us assume that (5 + 3√2) is a rational number. This means that:

Where “a” and “b” have an HCF as 1.

This is a contradiction as it is given in the question that √2 is an irrational number, which means that it can not be expressed as a fraction of two numbers “a” and “b” with HCF as 1.

∴ Our initial hypothesis stands rejected.

Hence, (5 + 3√2) is an irrational number.