# Prove that 2 − 3 √ 5 is an Irrational Number. - Mathematics

Numerical

Prove that $2 - 3\sqrt{5}$ is an irrational number.

#### Solution

Let us assume that $2 - 3\sqrt{5}$ is rational .Then, there exist positive co primes a and b such that

2-3sqrt5=a/b

3sqrt5=a/b-2

3sqrt5=(a/b-2)/3

sqrt5=(a-2b)/(3b)

This contradicts the fact sqrt5 is an irrational number

Hence 2-3sqrt5 is irrational

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 1 Real Numbers
Exercise 1.5 | Q 8 | Page 49