Question

How do you simplify $\dfrac{{\sqrt 4 }}{{36}}$?

Answer 1

Hint: First, take the square root of the numerator. E.g., $\sqrt {25} = \pm 5$. Here in order to simplify we mean that we need to cancel the numerator and denominator with their common factor unless they are not able to be canceled further. Hence, we need to apply the same method in order to solve this problem.

Complete step-by-step solution:
Here we are given to simplify the given fraction which is given as $\dfrac{{\sqrt 4 }}{{36}}$.
A fraction is a number that represents a part of a group. It is written as $\dfrac{a}{b}$, where a is called the numerator and b is called the denominator. The group is divided into b equal parts.
So we need to convert it into the simplest form which means that we need to cancel the numerator and denominator with their common factor unless they are not able to be canceled further.
We have to reduce $\dfrac{{\sqrt 4 }}{{36}}$ in the simplest form.
Apply square root in the numerator,
$ \Rightarrow \dfrac{{\sqrt 4 }}{{36}} = \dfrac{{ \pm 2}}{{36}}$
So we need to see if the numerator which is 2 and the denominator that is 36 have the common factor which means we need to cancel them by the number that can divide both the numerator and denominator completely.
So we know that 2 and 36 have the common factor that is 2 as both are divisible by this number 2 and we can cancel them with this number.
$ \Rightarrow \dfrac{{\sqrt 4 }}{{36}} = \pm \dfrac{1}{{18}}$

Hence, we have expressed $\dfrac{{\sqrt 4 }}{{36}}$ as a fraction in simplest form as $ \pm \dfrac{1}{{18}}$.

Note: Here the student must keep in mind that we do not have to divide this number and get the decimal answer but we have to just simplify and keep it as the form of the fraction which means that the numerator and denominator must be there.