Q. 166 - Intermediate Algebra

Question

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

(a) $7\sqrt{2}-3\sqrt{2}$

(b) $7\sqrt[3]{p}+2\sqrt[3]{p}$

(c) $5\sqrt[3]{x}-3\sqrt[3]{x}$

Step-by-Step Solution

Answer

The values are-

(a) $4\sqrt{2}$

(b) $9\sqrt[3]{p}$

(c) $2\sqrt[3]{x}$

Step 1. Solving for part (a)

We have $7\sqrt{2}-3\sqrt{2}$.

Subtract, because they are like terms.

This will give us,

$$\begin{gathered} =7\sqrt{2}-3\sqrt{2} \\ =4\sqrt{2} \end{gathered}$$

Step 2. Solving for part (b)

We have $7\sqrt[3]{p}+2\sqrt[3]{p}$.

Add, because they are like terms.

This will give us,

$$\begin{gathered} =7\sqrt[3]{p}+2\sqrt[3]{p} \\ =9\sqrt[3]{p} \end{gathered}$$

Step 3. Solving for part (c)

We have $5\sqrt[3]{x}-3\sqrt[3]{x}$.

Subtract, because they are like terms.

This will give us,

$$\begin{gathered} =5\sqrt[3]{x}-3\sqrt[3]{x} \\ =2\sqrt[3]{x} \end{gathered}$$