Question

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

Answer 1

Answer:

Simplifying the given expression gives;

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

Explanation:

Given the expression;

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

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

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

Therefore, simplifying the given expression gives;

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