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 \(\sqrt[3]{-a}=-\sqrt[3]{a}\) for any real number \(a\). So, \(\sqrt[3]{-2}=-\sqrt[3]{2}\). Then the original expression \(- 3\sqrt[3]{2}+2\sqrt[3]{2}+3\sqrt[3]{-2}\) becomes \(-3\sqrt[3]{2}+2\sqrt[3]{2}+3\times(-\sqrt[3]{2})\)

Step2: Combine like terms

First, expand the third term: \(3\times(-\sqrt[3]{2})=-3\sqrt[3]{2}\). Now the expression is \(-3\sqrt[3]{2}+2\sqrt[3]{2}-3\sqrt[3]{2}\). Combine the coefficients of \(\sqrt[3]{2}\): \((-3 + 2-3)\sqrt[3]{2}\)
Calculate the sum of the coefficients: \(-3+2=-1\), then \(-1 - 3=-4\). So the simplified form is \(-4\sqrt[3]{2}\)

Answer:

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