Question

Simplify the expression below by rationalizing the denominator. Leave your answer in exact form \frac{a \sqrt[]{b}}{c} . \sqrt[]{ \frac{81}{5} } simplifies to \frac{a \sqrt[]{b}}{c} Our value for a is AnswerOur value for b is AnswerOur value for c is Answer

Answer 1

The values for a, b and c are;

`\begin{gathered} a=9 \\ b=5 \\ c=5 \end{gathered}`

Step-by-step explanation:

Given the expression;

`\sqrt[]{(81)/(5)}`

To simplify;

`\frac{\sqrt[]{81}}{\sqrt[]{5}}=\frac{9}{\sqrt[]{5}}`

Rationalizing, we have;

`\frac{9}{\sqrt[]{5}}*\frac{\sqrt[]{5}}{\sqrt[]{5}}=\frac{9\sqrt[]{5}}{5}`

Expressing the expression in the form;

`\frac{a\sqrt[]{b}}{c}=\frac{9\sqrt[]{5}}{5}`

Therefore, the values for a, b and c are;

`\begin{gathered} a=9 \\ b=5 \\ c=5 \end{gathered}`