lunnatican4

2021-12-10

In the following, simplify using absolute value signs as needed.
$\sqrt{96{r}^{3}{s}^{3}}$

turtletalk75

Given information: An expression is given as $\sqrt{96{r}^{3}{s}^{3}}$.
Calculations: We have been given an expression is $\sqrt{96{r}^{3}{s}^{3}}$.
To simplify the radical expressions by using absolute value as needed, we must know about the radical properties and the index value of root is even or odd as shown below:
We know that, ${\left(ab\right)}^{m}={a}^{m}\cdot {b}^{m}$ and the corresponding product property of radical expression is $\sqrt[n]{ab}=\sqrt[n]{a}\cdot \sqrt[n]{b}$.
$⇒\sqrt{96{r}^{3}{s}^{3}}$ [Simplify the square root of $96{r}^{3}{s}^{3}$ with radical properties]
$⇒\sqrt{16{r}^{2}\cdot {s}^{2}\cdot 6rs}$ [Rewrite $96{r}^{3}{s}^{3}=16{r}^{2}\cdot {s}^{2}\cdot 6rs$]
$⇒\sqrt{{\left(4rs\right)}^{2}}\cdot \sqrt{6rs}$ [By using radical property $\sqrt[n]{ab}=\sqrt[n]{a}\cdot \sqrt[n]{b}$]
$⇒2|rs|\sqrt{6rs}$ [$\sqrt[n]{{a}^{n}}=|a|$, if the value of index is even]
Hence, the simplification of

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