Q. 8.86 - Intermediate Algebra

Question

Simplify-

(a) $(2-3\sqrt{11})(4-\sqrt{11})$

(b) $(\sqrt[3]{x}+1)(\sqrt[3]{x}+3)$

Step-by-Step Solution

Answer

The values are-

(a) $41-14\sqrt{11}$

(b) $\sqrt[3]{x^2}+4\sqrt[3]{x}+3$

Step 1. Explanation

(a) We will firstly multiply the terms with each other and then simplify them to get the value.

(b) we will firstly multiply the terms with each other and then simplifying the expression will give us the value.

Step 2. Solving for part (a)

We have $(2-3\sqrt{11})(4-\sqrt{11})$.

Multiplying the terms,

$$\begin{gathered} =8-2\sqrt{11}-12\sqrt{11}+3·11 \\ =8-2\sqrt{11}-12\sqrt{11}+33 \\ =41-14\sqrt{11} \end{gathered}$$

Thus we get the value as $41-14\sqrt{11}$.

Step 3. Solving for part (b)

We have $(\sqrt[3]{x}+1)(\sqrt[3]{x}+3)$ .

Multiplying the terms,

$$\begin{gathered} =\sqrt[3]{x^2}+3\sqrt[3]{x}+\sqrt[3]{x}+3 \\ =\sqrt[3]{x^2}+4\sqrt[3]{x}+3 \end{gathered}$$

Thus we get the value as $\sqrt[3]{x^2}+4\sqrt[3]{x}+3$.