Question

√2 is a irrational number prove ​

Answer 1

Answer:

√2 is irrational.

Step-by-step explanation:

Let's assume √2 is rational

So, √2 = p/q (as rational no. can be written in the form p/q ; p & q do not have common factors)

Squaring both sides

2 = p²/q²

p² = 2q²

p² is divisible by 2 so p is also divisible by 2...(1)

So we can write p as 2k

putting 2k in place of p

(2k)² = 2q²

4k² = 2q²

q² = 2k²

q² is divisible by 2 so q is also divisible by 2...(2)

p&q both are having common factors

this contradicts the fact that p & q should not have common factors.

This shows that √2 is irrational

Answer 2

Step-by-step explanation:

let √2 be a rational no.

√2=a/b

do square of both sides

2=a2/b2

2b2=a2

it means that a2 is multiple of b2

also a is multiple of b

let b=2c

2(2c)2=a2

8c2=a2

a2 is multiple of c2

also a is multiple of c

a is also multiple of b

it means that our assumption is wrong

therefore √2 is an irrational no.

hope u understand