Question

prove 3root2is irrational
no.

Answer 1

hey dear,


good evening,

if possible,let 3√2 is rational.

now,

we can write 3√2 as a/b.

thus,
$3 \sqrt{2} = a \div b$
now, cross multiplying it,we get

$a = 3 \sqrt{2} b$
again,

$a \div 3b = \sqrt{2}$
now,

a,3,b is rational.



Hence,


√2 is rational.


This contradicts the fact that √2 is irrational.


It happened due to our assumption that 3√2 is rational.


Hence,3√2 is irrational.



Thanks.