Question

How do you simplify $\dfrac{3}{\sqrt{3}}$ ?

Answer 1

Hint: To simplify a fraction we should simply divide the numerator by its denominator. Now to simplify the fractions with square roots we should have a proper grasp of squares and square roots.

Complete Step By Step Solution:
According to the given information, we need to turn $\dfrac{3}{\sqrt{3}}$ into its simplest form.
One possible way to rewrite$\dfrac{3}{\sqrt{3}}$ is $3\div \sqrt{3}$.
$\sqrt{3}$ is an irrational number which simply means that it cannot be written as a simple fraction.
But as we know $3$is simply the square of $\sqrt{3}$.
Hence we can write it as, $3=\sqrt{3}\times \sqrt{3}$,
We can write our equation as,
$\dfrac{\sqrt{3}\times \sqrt{3}}{\sqrt{3}}$
$\Rightarrow \sqrt{3}$

Hence, the simplest form of $\dfrac{3}{\sqrt{3}}$ is $\sqrt{3}$.

Note:
It is always better to have good knowledge of squares and square roots to solve such questions. We can also see that $\sqrt{3}$ is an irrational number which simply means that it cannot be written as a simple fraction. And also while dividing we should pay extra attention to any calculation mistake.