Question

prove that 1 / root 2 is an irrational number

Answer 1

Let 1/ root 2 is a rational no. and equal to r(where r is also a rational no. ).

$1 \div \sqrt{2} = r$
$1 = \sqrt{2} r$
Now,
LHS is a rational no. but RHS is an irrational no.
So,
our assumption was wrong.
and
$1 \div \sqrt{2} is \: no t \: a \: rational \: no.$
Therefore, it is a irrational no.
Hence, Proved.

Hope this will help you.....

☆☆ @ Mr. Thakur ☆☆