Question

which is equivalent to \\(\sqrt{\frac{24p^6q^7}{2pq}}\\)?
options:
\\(3p^3q^2\sqrt{2p}\\)
\\(2p^2q^3\sqrt{3p}\\)
\\(2p^3q^2\sqrt{3p}\\)
\\(3p^2q^3\sqrt{2p}\\)

Explanation:

Step1: Simplify fraction inside root

$\sqrt{\frac{24p^6q^7}{2pq}} = \sqrt{12p^{6-1}q^{7-1}} = \sqrt{12p^5q^6}$

Step2: Split into perfect squares/remainder

$\sqrt{4 \times 3 \times p^4 \times p \times q^6} = \sqrt{4p^4q^6} \times \sqrt{3p}$

Step3: Simplify perfect square root

$\sqrt{4p^4q^6} = 2p^2q^3$

Step4: Combine terms

$2p^2q^3\sqrt{3p}$

Answer:

B. $2p^2q^3\sqrt{3p}$