CBSE · Class 6-12

Back to Real Numbers

Class 10 · Mathematics (Basic) · Unit 1: Real Numbers

Proving Irrationality

Lesson 3 of 5

To prove

\sqrt{p}

(with

p

prime) is irrational, assume

\sqrt{p} = a/b

with

\gcd(a,b)=1

. Squaring gives

pb^2 = a^2

, so

p\mid a^2 \Rightarrow p\mid a

. Write

a = pk

: then

b^2 = pk^2

, so

p\mid b

. This contradicts

\gcd(a,b)=1

.

HCF and LCM by Prime Factorisation

Decimal Expansions of Rationals

All lessons in this unit