Respuesta :
Answer:
[tex]4\sqrt{5}[/tex]
Step-by-step explanation:
We are asked to write [tex]\sqrt{80}[/tex] in the simplest form.
We can write 80 as product of 16 and 5.
[tex]\sqrt{80}=\sqrt{16\cdot 5}[/tex]
Using radical rule [tex]\sqrt{m\cdot n}=\sqrt{m}\cdot \sqrt{n}[/tex], we will get:
[tex]\sqrt{16\cdot 5}=\sqrt{16}\cdot \sqrt{5}[/tex]
[tex]\sqrt{16\cdot 5}=\sqrt{4^2}\cdot \sqrt{5}[/tex]
[tex]\sqrt{16\cdot 5}=4\sqrt{5}[/tex]
Therefore, the simplest form of the given expression would be [tex]4\sqrt{5}[/tex].
The simplest form any expression can be determined by performing the basic mathematical operations and by converting it into its standard form.
The simplest from of [tex]\sqrt{80}[/tex] is [tex]4\sqrt{5}[/tex].
Given information:
The given root is [tex]\sqrt{80}[/tex]
as, we know a the property of root is
[tex]\sqrt{a \times b}=\sqrt{a}\times\sqrt{b}[/tex]
Also the term 80 can be simplified as:
[tex]80=16\times5[/tex]
So, using above information we can write:
[tex]\sqrt{80}=\sqrt{16}.\sqrt{5} \\\sqrt{80}=\sqrt{4^2}. \sqrt{5}\\\sqrt{80}=4\sqrt{5}\\[/tex]
Hence, the simplest from of [tex]\sqrt{80}[/tex] is [tex]4\sqrt{5}[/tex].
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