Question

Can I get a in depth explanation to simplifying non perfect roots with quotients? Ex: image

Answer 1

To get the answer, we will attempt to simplify the first expression into its simplest format.

$\sqrt[]{\frac{126xy^5}{32x^3}}$

We begin by dividing both the numerator and the denominator by 2:

$\sqrt[]{\frac{63xy^5}{16x^3}}$

Since x appears in both the numerator and the denominator, we can simplify such that

$\frac{x}{x^3}=\frac{1}{x^2}$

Hence, we have the expression to be

$\sqrt[]{\frac{63y^5}{16x^2}}$

Let us compare the both expressions to each other now:

$\sqrt[]{\frac{63y^5}{16x^2}}=\sqrt[]{\frac{63y^5}{ax^b}}$

Therefore,

$\begin{gathered} a=16 \\ b=2 \end{gathered}$