Question

Simplify the expression below by rationalizing the denominator. Leave your answer in exact form \frac{a+b\sqrt[]{c}}{d} . When typing your answer be sure to be careful and include the correct signs. \frac{5}{1+ \sqrt[]{3} } simplifies to \frac{a+b\sqrt[]{c}}{d} Our value for a is AnswerOur value for b is AnswerOur value for c is AnswerOur value for d is

Answer 1

Given the expression:

`\frac{5}{1+\sqrt[]{3}}`

We will simplify the given expression to:

`\frac{a+b\sqrt[]{c}}{d}`

The simplification will be as follows:

`\frac{5}{1+ \sqrt[]{3} }*\frac{1-\sqrt[]{3}}{1-\sqrt[]{3}}=\frac{5\cdot(1-\sqrt[]{3})}{1^2-(\sqrt[]{3})^2}=\frac{5\cdot1-5\cdot\sqrt[]{3}}{1-3}=\frac{5-5\sqrt[]{3}}{-2}`

Compare the result with

`\frac{a+b\sqrt[]{c}}{d}`

So, the answer will be:

`\begin{gathered} a=5 \\ b=-5 \\ c=3 \\ d=-2 \end{gathered}`