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

Sagot :

Answer:

Simplifying the given expression gives;

[tex]27+12\sqrt[]{5}[/tex]

Explanation:

Given the expression;

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

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

[tex]\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}[/tex]

Therefore, simplifying the given expression gives;

[tex]27+12\sqrt[]{5}[/tex]

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