Question

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

Explanation:

Step1: Simplify the cube root of negative number

Recall that for odd roots, \(\sqrt[3]{-a}=-\sqrt[3]{a}\). So, \(3\sqrt[3]{-2}=3\times(-\sqrt[3]{2})=-3\sqrt[3]{2}\).

Step2: Combine like terms

Now, substitute back into the original expression: \(-3\sqrt[3]{2}+2\sqrt[3]{2}-3\sqrt[3]{2}\).
Combine the coefficients: \((-3 + 2- 3)\sqrt[3]{2}\).
Calculate the sum of the coefficients: \(-3+2=-1\), then \(-1 - 3=-4\). So, the expression simplifies to \(-4\sqrt[3]{2}\).

Answer:

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