Question

1. $sqrt3{-108p^{12}q^{4}} = $

Explanation:

Step1: Factor radicand into cubes

$\sqrt[3]{-27 \times 4 \times p^{12} \times q^3 \times q}$

Step2: Separate cube factors

$\sqrt[3]{-27} \times \sqrt[3]{p^{12}} \times \sqrt[3]{q^3} \times \sqrt[3]{4q}$

Step3: Simplify cube roots

$-3 \times p^4 \times q \times \sqrt[3]{4q}$

Step4: Combine terms

$-3p^4q\sqrt[3]{4q}$

Answer:

$-3p^4q\sqrt[3]{4q}$