Question

Simplify the following expression by multiplying by theconjugate:6+3/5√5-2

Answer 1

Simplifying the given expression gives;

`27+12\sqrt[]{5}`

Step-by-step explanation:

Given the expression;

`\frac{6+3\sqrt[]{5}}{\sqrt[]{5}-2}`

Multiplying both the denominator and numerator by the conjugate of the denominator;

`\begin{gathered} \frac{6+3\sqrt[]{5}}{\sqrt[]{5}-2}*\frac{\sqrt[]{5}+2}{\sqrt[]{5}+2}=\frac{(6+3\sqrt[]{5})(\sqrt[]{5}+2)}{(\sqrt[]{5}-2)(\sqrt[]{5}+2)} \\ =\frac{6\sqrt[]{5}+6\sqrt[]{5}+12+3(5)}{5-4} \\ =\frac{12\sqrt[]{5}+12+15}{1} \\ =27+12\sqrt[]{5} \end{gathered}`

Therefore, simplifying the given expression gives;

`27+12\sqrt[]{5}`