Respuesta :

gmany

Answer:

[tex]\large\boxed{\sqrt{-36}+\sqrt{-100}+7=7+16i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\=====================\\\\\sqrt{-36}=\sqrt{(36)(-1)}=\sqrt{36}\cdot\sqrT{-1}=6i\\\sqrt{-100}=\sqrt{(100)(-1)}=\sqrt{100}\cdot\sqrt{-1}=10i\\\\\sqrt{-36}+\sqrt{-100}+7=6i+10i+7=7+16i[/tex]

Answer:

The answer is [tex]16i+7[/tex]

Step-by-step explanation:

In order to determine the answer, we have to know about imaginary numbers.

The imaginary numbers are different to real numbers because they use a new unit called "imaginary unit":

[tex]i=\sqrt{-1}[/tex]

i: imaginary unit

This new unit is applied like a factor when we have even roots with negative numbers inside.

In this case:

[tex]\sqrt{-36}=\sqrt{-1}*\sqrt{36}=6i\\\sqrt{-100}=\sqrt{-1}*\sqrt{100}=10i\\   \\\sqrt{-36}+\sqrt{-100}+7\\ 6i+10i+7\\16i+7[/tex]

Finally, the answer is [tex]16i+7[/tex]

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