Question

show that
$\sqrt{2}$
is an irrational number​

Answer 1

To prove √2 is an irrational number.

Suppose :-

√2 = $\frac{p}{q}$ ( p & q are integers and q $\cancel{=}0 and p and q have no common factor other than 1$

√2 = $\frac{p÷r}{q÷r}$=$\frac{a}{b}$

√2 = $\frac{a}{b}$

squaring both side

$(√2)^2$ = $\frac{a^2}{b^2}$

$2b^2 = a^2$

$a^2$ is multiple of 2 means a is also multiple of 2.

Answer 2

Answer:

Please look in the attachment.