Marla Payton

2021-12-06

In the following, simplify using absolute values signs as needed.

$\sqrt{80{s}^{15}}$

aquariump9

Beginner2021-12-07Added 40 answers

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 $\sqrt{n}\left\{ab\right\}=\sqrt{n}\left\{a\right\}\cdot \sqrt{n}\left\{b\right\}$ .

$\Rightarrow \sqrt{80{s}^{15}}$ [Simplify the square root of $80{s}^{15}$ with radical properties]

$\Rightarrow \sqrt{16{s}^{14}\cdot 5s}$ [Rewrite $80{s}^{15}=16{s}^{14}\cdot 5s$ ]

$\Rightarrow \sqrt{16{s}^{14}}\cdot \sqrt{5s}$ [By using radical property $\sqrt{n}\left\{ab\right\}=\sqrt{n}\left\{a\right\}\cdot \sqrt{n}\left\{b\right\}$ ]

$\Rightarrow 4\left|{s}^{7}\right|\sqrt{5s}$ [$\sqrt{n}\left\{{a}^{n}\right\}=\left|a\right|$ , if the value of index is even]

Hence, the simplification of$\sqrt{80{s}^{15}}\text{}is\text{}4\left|{s}^{7}\right|\sqrt{5s}$

Calculations: We have been given an expression is

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,

Hence, the simplification of