Question

Express as a fraction in simplest form with a rational denominator. 15

Answer 1

Step-by-step explanation

Given the expression

`\frac{4}{3-\sqrt[]{5}}`

We can find the simplified format below

`\begin{gathered} \frac{4}{3-\sqrt[]{5}} \\ \mathrm{Multiply\: by\: the\: conjugate}\: (3+√(5))/(3+√(5)) \\ =(4\left(3+√(5)\right))/(\left(3-√(5)\right)\left(3+√(5)\right)) \\ =\frac{12+4\sqrt[]{5}}{9+3\sqrt[]{5}-3\sqrt[]{5}-\sqrt[]{25}} \\ =\frac{12+4\sqrt[]{5}}{9-5} \\ =\frac{12+4\sqrt[]{5}}{4} \\ =\frac{4(3+\sqrt[]{5})}{4} \\ =3+\sqrt[]{5} \end{gathered}`

Answer:

`3+\sqrt[]{5}`