Multiply the radical expressions and simplify your answer. $\sqrt { 5 x ^ { 3 } } \cdot \sqrt { 18 x ^ { 6 } }$
A) $3 \sqrt { 10 x ^ { 9 } }$
B) $\sqrt { 30 x ^ { 9 } }$
C) $3 x ^ { 4 } \sqrt { 10 x }$
D) $9 x ^ { 4 } \sqrt { 10 x }$

Question

Quizplus · Accepted Answer

When multiplying radicals, you multiply the numbers inside the radicals together and the numbers outside the radicals together. Here, $\sqrt{5x^3} \cdot \sqrt{18x^6} = \sqrt{90x^9}$. Simplifying inside the radical, $90 = 9 \cdot 10$ and $x^9 = x^4 \cdot x^4 \cdot x$, so we can take out $9$ and $x^4$ as they are perfect squares, leaving us with $3x^4\sqrt{10x}$.

Multiply the Radical Expressions and Simplify Your Answer 5x3⋅18x6\sqrt { 5 x ^ { 3 } } \cdot \sqrt { 18 x ^ { 6 } }5x3​⋅18x6​

Multiply the Radical Expressions and Simplify Your Answer $\sqrt { 5 x ^ { 3 } } \cdot \sqrt { 18 x ^ { 6 } }$