Answer
$18$
Work Step by Step
$$\eqalign{
& \mathop {\lim }\limits_{x \to 3} \root 3 \of {x + 5} \left( {2{x^2} - 3x} \right) \cr
& \cr
& {\text{Use the Product Law}} \cr
& \mathop {\lim }\limits_{x \to a} \left[ {f\left( x \right)g\left( x \right)} \right] = \mathop {\lim }\limits_{x \to a} f\left( x \right) \cdot \mathop {\lim }\limits_{x \to a} g\left( x \right) \cr
& \mathop {\lim }\limits_{x \to 3} \root 3 \of {x + 5} \left( {2{x^2} - 3x} \right) = \left[ {\mathop {\lim }\limits_{x \to 3} \root 3 \of {x + 5} } \right]\left[ {\mathop {\lim }\limits_{x \to 3} \left( {2{x^2} - 3x} \right)} \right] \cr
& \cr
& {\text{Use the Root Law }}\mathop {\lim }\limits_{x \to a} \root n \of {f\left( x \right)} = \root n \of {\mathop {\lim }\limits_{x \to a} f\left( x \right)} ,{\text{ }}n{\text{ }} \in {\text{ Z + }} \cr
& and{\text{ Use the Sum and Difference Laws }} \cr
& = \left[ {\root 3 \of {\mathop {\lim }\limits_{x \to 3} \left( {x + 5} \right)} } \right]\left[ {\mathop {\lim }\limits_{x \to 3} \left( {2{x^2}} \right) - \mathop {\lim }\limits_{x \to 3} \left( {3x} \right)} \right] \cr
& = \left[ {\root 3 \of {\mathop {\lim }\limits_{x \to 3} \left( x \right) + \mathop {\lim }\limits_{x \to 3} \left( 5 \right)} } \right]\left[ {\mathop {\lim }\limits_{x \to 3} \left( {2{x^2}} \right) - \mathop {\lim }\limits_{x \to 3} \left( {3x} \right)} \right] \cr
& \cr
& {\text{Use the Constant Multiple Law }} \cr
& \mathop {\lim }\limits_{x \to a} \left[ {cf\left( x \right)} \right] = c\mathop {\lim }\limits_{x \to a} f\left( x \right) \cr
& = \left[ {\root 3 \of {\mathop {\lim }\limits_{x \to 3} \left( x \right) + \mathop {\lim }\limits_{x \to 3} \left( 5 \right)} } \right]\left[ {\mathop {2\lim }\limits_{x \to 3} \left( {{x^2}} \right) - 3\mathop {\lim }\limits_{x \to 3} \left( x \right)} \right] \cr
& \cr
& {\text{Use The power Law }}\mathop {\lim }\limits_{x \to a} {x^n} = {a^n}{\text{, }}n{\text{ is a positive integer }} \cr
& {\text{and the laws }}\mathop {\lim }\limits_{x \to a} x = a,{\text{ }}\mathop {\lim }\limits_{x \to a} c = c,{\text{ then}} \cr
& = \left[ {\root 3 \of {\left( 3 \right) + \left( 5 \right)} } \right]\left[ {2{{\left( 3 \right)}^2} - 3\left( 3 \right)} \right] \cr
& {\text{Simplifying}} \cr
& = \left[ {\root 3 \of 8 } \right]\left[ 9 \right] \cr
& = 18 \cr} $$
