Q. 167 - Intermediate Algebra

Question

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

(a) $3\sqrt{5}+6\sqrt{5}$

(b) $9\sqrt[3]{a}+3\sqrt[3]{a}$

(c) $5\sqrt[4]{2z}+\sqrt[4]{2z}$

Step-by-Step Solution

Answer

The values are-

(a) $9\sqrt{5}$

(b) $12\sqrt[3]{a}$

(c) $6\sqrt[4]{2z}$

Step 1. Solving for part (a)

We have $3\sqrt{5}+6\sqrt{5}$.

Add, because they are like terms.

This will give us,

$$\begin{gathered} =3\sqrt{5}+6\sqrt{5} \\ =9\sqrt{5} \end{gathered}$$

Step 2. Solving for part (b)

We have $9\sqrt[3]{a}+3\sqrt[3]{a}$.

Add, because they are like terms.

This will give us,

$$\begin{gathered} =9\sqrt[3]{a}+3\sqrt[3]{a} \\ =12\sqrt[3]{a} \end{gathered}$$

Step 3. Solving for part (c)

We have $5\sqrt[4]{2z}+\sqrt[4]{2z}$.

Add, because they are like terms.

This will give us,

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