Question

prove that √2 is irrational tell me fast

Answer 1

hope it helps u............

Answer 2

Hey there!

Prove that √2 is irrational

Let us assume the contrary, that is √2 is rational.

Then,

$\sqrt{2} = \frac{a}{b}$

where a and b are co-primes and b≠0

$2 = \frac{a {}^{2} }{b {}^{2} }$

(by squaring both sides)

$a {}^{2} = 2b {}^{2}$

2 is a factor of a ²,
so, 2 is also a factor of a

$a = 2c$

$(2c) {}^{2} = 2b {}^{2}$

$4c {}^{2} = 2b {}^{2}$

$2c {}^{2} = b {}^{2}$

So, b is a factor of 2

Since a and b are having 2 as common factor, this contradicts our assunption that a and b are co-primes.

So, √2 is not rational

Hence,  √2 is irrational.

Hope it helps!