Q. 8.19 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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

Part (a) Step 1. Given information

The root: $\sqrt{64x^2}$

Part (a) Step 2. Calculation

We have,

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

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,

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

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