Q. 171 - Intermediate Algebra

Question

Add and subtract radical expressions in the following exercises, simplify.  

(a) $8\sqrt{3c}+2\sqrt{3c}-9\sqrt{3c}$
(b) $2\sqrt[3]{4pq}-5\sqrt[3]{4pq}+4\sqrt[3]{4pq}$

Step-by-Step Solution

Answer

The values are-

(a) $\sqrt{3c}$

(b) $\sqrt[3]{4pq}$

Step 1. Solving for part (a)

We have $8\sqrt{3c}+2\sqrt{3c}-9\sqrt{3c}$.

Combine, because they are like terms.

This will give us,

$$\begin{gathered} =8\sqrt{3c}+2\sqrt{3c}-9\sqrt{3c} \\ =10\sqrt{3c}-9\sqrt{3c} \\ =\sqrt{3c} \end{gathered}$$

Step 2. Solving for part (b)

We have $2\sqrt[3]{4pq}-5\sqrt[3]{4pq}+4\sqrt[3]{4pq}$.

Combine, because they are like terms.

This will give us,

$$\begin{gathered} =2\sqrt[3]{4pq}-5\sqrt[3]{4pq}+4\sqrt[3]{4pq} \\ =6\sqrt[3]{4pq}-5\sqrt[3]{4pq} \\ =\sqrt[3]{4pq} \end{gathered}$$