Question

What is $6$ divided by the square root of three in simplest radical form?

Answer 1

Hint: Generally, in these types of questions first we remove radical signs from the denominator. To do that we have to do the rationalization in the given question. At last, we will move the integral part inside the radical sign.

Complete step by step answer:
 In the above question, it is given that $\dfrac{6}{{\sqrt 3 }}$.
Now we will rationalize the above term.
On rationalizing, we get
$ \Rightarrow \dfrac{6}{{\sqrt 3 }}\dfrac{{\sqrt 3 }}{{\sqrt 3 }}$
On multiplication in denominator, we get
$ \Rightarrow \dfrac{{6\sqrt 3 }}{3}$
On division, we get
$ \Rightarrow 2\sqrt 3 $
Now we can also write the above equation as,
\[ \Rightarrow \sqrt 2 \times \sqrt 2 \times \sqrt 3 \]
Therefore, on multiplication, we get
$ \Rightarrow \sqrt {12} $

Note:
 Expressing in the simplest radical form just means simplifying a radical so that there are no more square roots, cube roots, $4th$ roots, etc left to find. It also means removing any radicals in the denominator of a fraction. A radical is a number that has a fraction as its exponent.