Question

Is 1/root 3 a rational number

Answer 1

$\huge{\mathfrak{Question}}$

You are is that is $\frac{1}{\sqrt{3}}$ a Rational Number

$\huge\boxed{\mathfrak{Answer}}$

Let's Check this out.

Firstly, we know every rational number is in the form of $\frac{p}{q}$ where q ≠ 0.

Thus,

$\frac{1}{ \sqrt{3} } = \frac{p}{q}$

Now,

$\implies \sqrt{3} p = q$

$\implies \sqrt{3} = \frac{q}{p} \\ and \: we \: know \: that \: \sqrt{3} \: is \: irratinal$

Thus,

It will be also be Irrational $(\sqrt{3})^{-1}$

Hence, (Proved)

Answer 2

No, it is an Irrational Number.

Reason why...?

In the shortest form, we know, √3 is an irrational number.

So it will also mean that 1/√3 is an irrational number because irrational number divided by a rational number always gives an irrational number.

here, 1 is a rational number, and √3 is an irrational.