# Real Numbers - Irrational Numbers

Ex 1.3 Q2. CBSE 10th Maths NCERT exercise solution

#### Question: Prove that 3 + 2√5 is irrational.

So, we can express 3 + 2√5 = $\frac{a}{b}$ where a and b are co-prime integers and b ≠ 0.
So, 2√5 = $\frac{a}{b}$ – 3
Or, 2√5 = $\frac{a - 3b}{b}$
Hence, √5 = $\frac{a - 3b}{2b}$
Because a, b, 3 and 2 are integers, $\frac{a - 3b}{2b}$ is rational implying that √5 is irrational.