Question

0-8
Prove that 2 is irrational no.
$\sqrt{5}$
​

Answer 1

Answer:

let √2 = p/q

squaring both sides (√2)²= ( p/q)²

2=p²/q²

2q²=p²

As 2 is the factor of p² so it will be the factor of p also

let p = 2x

so,

2q² = (2x)²

2q² = 4x²(cut 4 by 2)

q² = 2x²

NOW 2 IS THE FACTOR OF p² AND q² so it will be the factor of p and q also.

HERE HCF OF p AND q IS 2 AND FOR BEING A RATIONAL NUMBER HCF MUST BE 1.

So, THE CONTRADICTION IS WRONG(√2=p/q)

SO √2 IS IRRATIONAL NUMBER.

Step-by-step explanation: