Multiply the radical expressions and simplify your answer.
-$( \sqrt { 108 } - 1 ) ( \sqrt { 3 } + 5 )$
A) 13
B) $13 + 29 \sqrt { 3 }$
C) $\sqrt { 321 } - 5$
D) $319 + 5 \sqrt { 108 } - \sqrt { 3 }$

Question

Quizplus · Accepted Answer

First, simplify $\sqrt{108}$ as $6\sqrt{3}$ because $108 = 36 \times 3$ and $\sqrt{36} = 6$. Then, multiply the expressions: $(6\sqrt{3} - 1)(\sqrt{3} + 5)$. Distribute to get $6\sqrt{3} \cdot \sqrt{3} + 30\sqrt{3} - \sqrt{3} - 5$, which simplifies to $18 + 29\sqrt{3} - 5$, resulting in $13 + 29\sqrt{3}$.

Multiply the Radical Expressions and Simplify Your Answer (108−1)(3+5)( \sqrt { 108 } - 1 ) ( \sqrt { 3 } + 5 )(108​−1)(3​+5)

Multiply the Radical Expressions and Simplify Your Answer $( \sqrt { 108 } - 1 ) ( \sqrt { 3 } + 5 )$