Q. 165 - Intermediate Algebra

Question

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

(a) $8\sqrt{2}-5\sqrt{2}$

(b) $5\sqrt[3]{m}+2\sqrt[3]{m}$

(c) $8\sqrt[4]{m}-2\sqrt[4]{m}$

Step-by-Step Solution

Answer

The values are-

(a) $3\sqrt{2}$

(b) $7\sqrt[3]{m}$

(c) $6\sqrt[4]{m}$

Step 1. Solving for part (a)

We have $8\sqrt{2}-5\sqrt{2}$.

Substract, because they are like terms.
This will give us,

$$\begin{gathered} =8\sqrt{2}-5\sqrt{2} \\ =3\sqrt{2} \end{gathered}$$

Step 2. Solving for part (b)

We have $5\sqrt[3]{m}+2\sqrt[3]{m}$.

Add, because they are like terms.

This will give us,

$$\begin{gathered} =5\sqrt[3]{m}+2\sqrt[3]{m} \\ =7\sqrt[3]{m} \end{gathered}$$

Step 3. Solving for part (c)

We have $8\sqrt[4]{m}-2\sqrt[4]{m}$.

Subtract, because they are like terms.

This will give us,

$$\begin{gathered} =8\sqrt[4]{m}-2\sqrt[4]{m} \\ =6\sqrt[4]{m} \end{gathered}$$