Q. 8.16 - Intermediate Algebra

Question

Simplify: $\left(a\right) \sqrt{m^4} \left(b\right) \sqrt{b^{10}}$

Step-by-Step Solution

Answer

The solution of (a) and (b) are $m^2 and \left|b^5\right|$ respectively.

Part (a) Step 1. Given information

The root: $\sqrt{m^4}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt{m^4} \\ =\sqrt{{\left(m^2\right)}^2} \sin ce {\left(m^2\right)}^2=m^4 \\ =m^2 \end{gathered}$$

In this case, the absolute value sign is not needed as $m^2$ is positive.

Therefore, the solution is $m^2$

Part (b) Step 1. Given information

The root: $\sqrt{b^{10}}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt{b^{10}} \\ =\sqrt{{\left(b^5\right)}^2} \sin ce {\left(b^5\right)}^2=b^{10} \\ =\left|b^5\right| \sin ce the index n is even \sqrt{a^n}=\left|a\right| \end{gathered}$$

Therefore, the solution is $\left|b^5\right|$