Question

Prove that 3 root 2 in irrational

Answer 1

Answer:-

Let us consider that 3root2 is a rational number. It can be written in the form p/q (p and q are co primes)

p/q = 3root2

p/3q = root2

Now,

p/3q = integer/interger

= rational number

But, this contradicts the fact that root2 is irrational.

Therefore, our assumption that 3root2 is rational is WRONG.

Hence, 3root2 is an irrational number.

Answer 2

Answer:

Let us consider that 3√2 is a rational number.

which means it can be written as

=p/q = 3√2

= p/3q = √2

Now,

p/3q = rational number

*But, this contradicts  that √2 is irrational.Therefore, our assumption.

Hence, 3√2 is an irrational number.

Thank U