Marla Payton

2021-12-06

In the following, simplify using absolute values signs as needed.
$\sqrt{80{s}^{15}}$

aquariump9

Given information: An expression is given as $\sqrt{80{s}^{15}}$.
Calculations: We have been given an expression is $\sqrt{80{s}^{15}}$.
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 $\sqrt{n}\left\{ab\right\}=\sqrt{n}\left\{a\right\}\cdot \sqrt{n}\left\{b\right\}$.
$⇒\sqrt{80{s}^{15}}$ [Simplify the square root of $80{s}^{15}$ with radical properties]
$⇒\sqrt{16{s}^{14}\cdot 5s}$ [Rewrite $80{s}^{15}=16{s}^{14}\cdot 5s$]
$⇒\sqrt{16{s}^{14}}\cdot \sqrt{5s}$ [By using radical property $\sqrt{n}\left\{ab\right\}=\sqrt{n}\left\{a\right\}\cdot \sqrt{n}\left\{b\right\}$]
$⇒4|{s}^{7}|\sqrt{5s}$ [$\sqrt{n}\left\{{a}^{n}\right\}=|a|$, if the value of index is even]
Hence, the simplification of

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