Question

prove that three root two is irrational​

Answer 1

Hey mate!

here is your answer:

step by step explanation:

We know that root 2 is irrational.

Let us assume to the contrary that 3 root 2 is rational and 3 root 2 =a/b where a and b are two co primes.

Now, 3 root 2 =a/b

So, root 2 =a/3b

We know that root 3 is irrational , thus w/3b will also be irrational.

But this contradicts our assumption that 3 root 2 is rational.

Thus , 3 root 2 is rational.

hope it helped^_^

Answer 2

$\mathfrak{Solution}$

Assume that 3 root 2 is ratinal.

So we can find two coprimes a and b, such that,

$3 \sqrt{2} = \frac{a}{b}$

where b not equal to zero.

$\sqrt{2} = \frac{a}{3b}$

Here LHS is irrational and RHS is rational, which is a condratiction.

This is due to our wrong assumption that 3 root 2 is rational

so, we conclude 3 root 2 as irrational.

$\mathit{HENCE\: PROVED}$