Question

Simplify:$\left(a\right)\sqrt{64x^2}\left(b\right)-\sqrt{100p^2}$

Short answer

The solution of (a) and (b) are$8\left|x\right|and-10\left|p\right|$ respectively

Step-by-step solution

Part (a) Step 1. Given information

The root:$\sqrt{64x^2}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt{64x^2} \\ =\sqrt{{\left(8x\right)}^2}\sin ce{\left(8x\right)}^2=64x^2 \\ =8\left|x\right|\sin cetheindexiseven\sqrt[n]{a^n}=\left|a\right| \end{gathered}$$

Therefore, the solution is$8\left|x\right|$

Part (b) Step 1. Given information

The root:$-\sqrt{100p^2}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} -\sqrt{100p^2} \\ =-\sqrt{{\left(10p\right)}^2}\sin ce{\left(10p\right)}^2=100p^2 \\ =-10\left|p\right|\sin cetheindexniseven\sqrt[n]{a^n}=\left|a\right| \end{gathered}$$

Therefore, the solution is$-10\left|p\right|$