Q. 170 - Intermediate Algebra

Question

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

(a) $\sqrt{11b}-5\sqrt{11b}+3\sqrt{11b}$
(b) $8\sqrt[4]{11cd}+5\sqrt[4]{11cd}-9\sqrt[4]{11cd}$

Step-by-Step Solution

Answer

The values are-

(a) $-\sqrt{11b}$
(b) $4\sqrt[4]{11cd}$

Step 1. Solving for part (a)

We have $\sqrt{11b}-5\sqrt{11b}+3\sqrt{11b}$.

Combine, because they are like terms.

This will give us,

$$\begin{gathered} =\sqrt{11b}-5\sqrt{11b}+3\sqrt{11b} \\ =4\sqrt{11b}-5\sqrt{11b} \\ =-\sqrt{11b} \end{gathered}$$

Step 2. Solving for part (b)

We have $8\sqrt[4]{11cd}+5\sqrt[4]{11cd}-9\sqrt[4]{11cd}$.

Combine, because they are like terms.

This will give us,

$$\begin{gathered} =8\sqrt[4]{11cd}+5\sqrt[4]{11cd}-9\sqrt[4]{11cd} \\ =13\sqrt[4]{11cd}-9\sqrt[4]{11cd} \\ =4\sqrt[4]{11cd} \end{gathered}$$