simplify: $sqrt3{108}$\na $9sqrt3{12}$\nb $4sqrt3{3}$\nc $3sqrt3{12}$\nd $3sqrt3{4}$

Explanation:

Step1: Prime - factorize 108

$108 = 2\times2\times3\times3\times3=2^{2}\times3^{3}$

Step2: Rewrite the cube - root

$\sqrt[3]{108}=\sqrt[3]{2^{2}\times3^{3}}$

Step3: Apply the cube - root property $\sqrt[3]{ab}=\sqrt[3]{a}\times\sqrt[3]{b}$

$\sqrt[3]{2^{2}\times3^{3}}=\sqrt[3]{3^{3}}\times\sqrt[3]{2^{2}}$

Step4: Simplify each cube - root

$\sqrt[3]{3^{3}} = 3$ and $\sqrt[3]{2^{2}}=\sqrt[3]{4}$, so $\sqrt[3]{108}=3\sqrt[3]{4}$

Answer:

D. $3\sqrt[3]{4}$