Express the radical in simplified form.Assume that all variables represent positive real numbers.
-$-\sqrt{405 k^{7} q^{8}}$
A) $9 \mathrm{k}^{7} \mathrm{q}^{8} \sqrt{5 \mathrm{k}}$
B) $-9 k^{3} q^{4} \sqrt{5 k}$
C) $-9 \mathrm{k}^{3} \mathrm{q}^{4} \sqrt{5}$
D) $9 \mathrm{k}^{3} \mathrm{q}^{4} \sqrt{5 \mathrm{k}}$

Question

Quizplus · Accepted Answer

First, factor 405 into $9 \times 45 = 9 \times 9 \times 5$, so $\sqrt{405} = 9\sqrt{5}$. For $k^7$, take $k^6$ out of the square root as $k^3$, leaving $k$ inside. For $q^8$, take $q^8$ out as $q^4$, leaving no $q$ inside. Combine these to get $-9k^3q^4\sqrt{5k}$.

Express the Radical in Simplified Form −405k7q8-\sqrt{405 k^{7} q^{8}}−405k7q8​ A) 9k7q85k9 \mathrm{k}^{7} \mathrm{q}^{8} \sqrt{5 \mathrm{k}}9k7q85k​

Express the Radical in Simplified Form $-\sqrt{405 k^{7} q^{8}}$ A) $9 \mathrm{k}^{7} \mathrm{q}^{8} \sqrt{5 \mathrm{k}}$