Q. 177 - Intermediate Algebra

Question

In the following exercises, simplify.

a.$\sqrt{72a^5}-\sqrt{50a^5}$

b.$9\sqrt[4]{80p^4}-6\sqrt[4]{405p^4}$

Step-by-Step Solution

Answer

On simplification, we get $a^2\sqrt{2a},0$ respectively

Part (a) Step 1: Given information

Given the expression $\sqrt{72a^5}-\sqrt{50a^5}$

Part (a) Step 2: Simplifying the radical and combine like terms

Simplifying radical and combining we get

$$\begin{gathered} \sqrt{72a^5}-\sqrt{50a^5}=\sqrt{36a^4·2a}-\sqrt{25a^4·2a} \\ \sqrt{72a^5}-\sqrt{50a^5}=\sqrt{36a^4}·\sqrt{2a}-\sqrt{25a^4}·\sqrt{2a} \\ \sqrt{72a^5}-\sqrt{50a^5}=6a^2\sqrt{2a}-5a^2\sqrt{2a} \\ \sqrt{72a^5}-\sqrt{50a^5}=a^2\sqrt{2a} \end{gathered}$$

Part (b) Step 1: Given information

Given expression $9\sqrt[4]{80p^4}-6\sqrt[4]{405p^4}$

Part (b) Step 2: Simplifying radical and solving

Simplifying, we get

$$\begin{gathered} 9\sqrt[4]{80p^4}-6\sqrt[4]{405p^4}=9\sqrt[4]{16p^4·5}-6\sqrt[4]{81p^4·5} \\ 9\sqrt[4]{80p^4}-6\sqrt[4]{405p^4}=9\sqrt[4]{16p^4}·\sqrt[4]{5}-6\sqrt[4]{81p^4}·\sqrt[4]{5} \\ 9\sqrt[4]{80p^4}-6\sqrt[4]{405p^4}=9·2·\sqrt[4]{5}-6·3·\sqrt[4]{5} \\ 9\sqrt[4]{80p^4}-6\sqrt[4]{405p^4}=18\sqrt[4]{5}-18\sqrt[4]{5} \\ 9\sqrt[4]{80p^4}-6\sqrt[4]{405p^4}=0 \end{gathered}$$