#### Answer

$3\sqrt[]{5}-6$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{3}{\sqrt[]{5}+2}
,$ multiply the numerator and the denominator by the conjugate of the denominator. Then use special products and the laws of radicals to simplify the result.
$\bf{\text{Solution Details:}}$
Multiplying the numerator and the denominator by the conjugate of the denominator results to
\begin{array}{l}\require{cancel}
\dfrac{3}{\sqrt[]{5}+2}\cdot\dfrac{\sqrt[]{5}-2}{\sqrt[]{5}-2}
\\\\=
\dfrac{3(\sqrt[]{5}-2)}{(\sqrt[]{5}+2)(\sqrt[]{5}-2)}
.\end{array}
Using the product of the sum and difference of like terms which is given by $(a+b)(a-b)=a^2-b^2,$ the expression above is equivalent
\begin{array}{l}\require{cancel}
\dfrac{3(\sqrt[]{5}-2)}{(\sqrt[]{5})^2-(2)^2}
\\\\=
\dfrac{3(\sqrt[]{5}-2)}{5-4}
\\\\=
\dfrac{3(\sqrt[]{5}-2)}{1}
\\\\=
3(\sqrt[]{5}-2)
.\end{array}
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
3(\sqrt[]{5})+3(-2)
\\\\=
3\sqrt[]{5}-6
.\end{array}