Question

1. \sqrt3{-108u^3v}

Explanation:

Step1: Factor radicand into perfect cubes

$\sqrt[3]{-27 \times 4 \times u^3 \times v}$

Step2: Split cube root into products

$\sqrt[3]{-27} \times \sqrt[3]{u^3} \times \sqrt[3]{4v}$

Step3: Simplify perfect cube roots

$-3 \times u \times \sqrt[3]{4v}$

Answer:

$-3u\sqrt[3]{4v}$