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[]{(126xy^5)/(32x^3)}`

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

`\sqrt[]{(63xy^5)/(16x^3)}`

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

`(x)/(x^3)=(1)/(x^2)`

Hence, we have the expression to be

`\sqrt[]{(63y^5)/(16x^2)}`

Let us compare the both expressions to each other now:

`\sqrt[]{(63y^5)/(16x^2)}=\sqrt[]{(63y^5)/(ax^b)}`

Therefore,

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