NCERT Solutions for Class 10 Maths Chapter 1

Important NCERT Questions

Real Numbers

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 1.3

Page No:14

Questions No:2

# Prove that 3 + 2√5 is irrational.

Share

Get Hindi Medium and English Medium NCERT Solution for Class 10 Maths to download.

Please follow the link to visit website for first and second term exams solutions.

https://www.tiwariacademy.com/ncert-solutions/class-10/maths/chapter-1/

Let 3+2√5 is rational.

Therefore, we can find two co-prime integers a, b (b ≠ 0) such that

3+2√5 = a/b

2√5 = (a/b)-3

√5 = 1/2((a/b) – 3)

Since a andbare integers, 1/2((a/b) – 3) will also be rational and therefore, √5 is rational.

This contradicts the fact that √5 is irrational. Hence, our assumption that 3 + 2√5 is rational is false. Therefore, 3 +2√5 is irrational.

See here 😇