guringpw

2021-12-06

In the following, simplify using absolute value signs as needed.
$\frac{2+\sqrt{40}}{2}$

Hattie Schaeffer

Given information: An expression is given as $\frac{2+\sqrt{40}}{2}$.
Calculations: We have been given an expression is $\frac{2+\sqrt{40}}{2}$.
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 $\sqrt{n}\left\{ab\right\}=\sqrt{n}\left\{a\right\}\cdot \sqrt{n}\left\{b\right\}$.
$⇒\frac{2+\sqrt{40}}{2}$ [Simplify the square root of 40 with radical properties]
$⇒\frac{2+\sqrt{4\cdot 10}}{2}$ [Rewrite 40=4*10]
$⇒\frac{2+\sqrt{4}\sqrt{10}}{2}$ [By using radical property $\sqrt{n}\left\{ab\right\}=\sqrt{n}\left\{a\right\}\cdot \sqrt{n}\left\{b\right\}$]
$⇒\frac{2+2\sqrt{10}}{2}$ [Product the two radicals i.e 2 and $\sqrt{10}$]
$\text{Undefined control sequence \cancel}$ [Remove the common factor from the numerator and denominator]
$⇒\left(1+\sqrt{10}\right)$ [Simplify]
Hence, the simplification of .

Do you have a similar question?