Question

simplify: $-3sqrt3{2} + 2sqrt3{2} + 3sqrt3{-2}$
a. $-4sqrt3{2}$
b. $-9sqrt3{2}$
c. $-12sqrt3{2}$
d. $-7sqrt3{2}$

Explanation:

Step1: Simplify the negative cube root

Recall that $\sqrt[3]{-x}=-\sqrt[3]{x}$. So $3\sqrt[3]{-2} = -3\sqrt[3]{2}$

Step2: Combine like terms

Group the terms with $\sqrt[3]{2}$:
$-3\sqrt[3]{2} + 2\sqrt[3]{2} - 3\sqrt[3]{2}$

Step3: Calculate the coefficient sum

Add the coefficients:
$(-3 + 2 - 3)\sqrt[3]{2} = -4\sqrt[3]{2}$

Answer:

A. $-4\sqrt[3]{2}$