guringpw

2021-12-06

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

$\frac{2+\sqrt{40}}{2}$

Hattie Schaeffer

Beginner2021-12-07Added 37 answers

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

$\Rightarrow \frac{2+\sqrt{40}}{2}$ [Simplify the square root of 40 with radical properties]

$\Rightarrow \frac{2+\sqrt{4\cdot 10}}{2}$ [Rewrite 40=4*10]

$\Rightarrow \frac{2+\sqrt{4}\sqrt{10}}{2}$ [By using radical property $\sqrt{n}\left\{ab\right\}=\sqrt{n}\left\{a\right\}\cdot \sqrt{n}\left\{b\right\}$ ]

$\Rightarrow \frac{2+2\sqrt{10}}{2}$ [Product the two radicals i.e 2 and $\sqrt{10}$ ]

$\text{Undefined control sequence cancel}$ [Remove the common factor from the numerator and denominator]

$\Rightarrow (1+\sqrt{10})$ [Simplify]

Hence, the simplification of$\frac{2+\sqrt{40}}{2}\text{}is\text{}(1+\sqrt{10})$ .

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

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