Question

prove that \sqrt2 is irrational​

Answer 1

Answer:

A proof that the square root of 2 is irrational. Let's suppose √2 is a rational number. Then we can write it √2 = a/b where a, b are whole numbers, b not zero. We additionally assume that this a/b is simplified to lowest terms, since that can obviously be done with any fraction.

Answer 2

Answer:

Step-by-step explanation:

Lets assume $\sqrt{2}$ is rational

Hence $\sqrt{2}$= a/b where a and b are two co prime numbers

$\sqrt{2}$b=a

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

2 | $a^{2}$

2 | a  hence 2 divides a

hence a=2c where c is any constant

$\sqrt{2}$b=2c

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

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

2 | $b^{2}$

2 | b

hence 2 divides b

but a and b are two co primes

hence our assumption was wrong

$\sqrt{2}$ is irrational