# Prove that 3 + 2√5 is irrational.

**Solution:**

Irrational numbers are the subset of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers and q ≠ 0.

We have to prove that 3 + 2√5 is irrational. We will be solving this question with the help of the contradiction method.

Let's assume that 3 + 2√5 is rational. If 3 + 2√5 is rational that means it can be written in the form of a/b where a and b are integers that have no common factor other than 1 and b ≠ 0.

3 + 2√5 = a/b

b(3 + 2√5) = a

3b + 2√5b = a

2√5b = a - 3b

√5 = (a - 3b)/2b

Since (a - 3b)/2b is a rational number, then √5 is also a rational number.

But, we know that √5 is irrational.

Therefore, our assumption was wrong that 3 + 2√5 is rational. Hence, 3 + 2√5 is irrational.

**Video Solution:**

## Prove that 3 + 2√5 is irrational.

### NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.3 Question 2 - Chapter 1 Exercise 1.3 Question 2:

**Summary:**

We have proved that 3 + 2√5 is irrational using the contradiction method.