Q. 168 - Intermediate Algebra

Question

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

(a) $4\sqrt{5}+8\sqrt{5}$

(b) $\sqrt[3]{m}-4\sqrt[3]{m}$

(c) $\sqrt{n}+3\sqrt{n}$

Step-by-Step Solution

Answer

The values are-

(a) $12\sqrt{5}$

(b) $-3\sqrt[3]{m}$

(c) $4\sqrt{n}$

Step 1. Solving for (a)

We have $4\sqrt{5}+8\sqrt{5}$.

Add, because they are like terms.

This will give us,

$$\begin{gathered} =4\sqrt{5}+8\sqrt{5} \\ =12\sqrt{5} \end{gathered}$$

Step 2. Solving for part (b)

We have $\sqrt[3]{m}-4\sqrt[3]{m}$.

Subtract, because they are like terms.

This will give us,

$$\begin{gathered} =\sqrt[3]{m}-4\sqrt[3]{m} \\ =-3\sqrt[3]{m} \end{gathered}$$

Step 3. Solving for part (c)

We have $\sqrt{n}+3\sqrt{n}$.

Add, because they are like terms.

This will give us,

$$\begin{gathered} =\sqrt{n}+3\sqrt{n} \\ =4\sqrt{n} \end{gathered}$$