Question

I need help writing this in simplest form. What is the square root of 16/81 in simplest form ?

Answer 1

We will have the following:

`\sqrt[]{(16)/(81)}=\frac{\sqrt[]{16}}{\sqrt[]{81}}=(4)/(9)`

So, the expression in its simplest form is 4/9.

***Explanation***

First we are given the expression:

`\sqrt[]{(16)/(81)}`

From the properties of roots, we will have that if a root contains a fraction, then we can rewrite the expression applying the root to the numerator and denominator [Separately], this is:

`\sqrt[]{(16)/(81)}=\frac{\sqrt[]{16}}{\sqrt[]{81}}`

Since, these expressions are equivalent, then we solve for each one, that is:

`\begin{cases}\sqrt[]{16}=4 \\ \& \\ \sqrt[]{81}=9\end{cases}`

Then, we simply replace in the fraction form:

`\sqrt[]{(16)/(81)}=(4)/(9)`