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Express the following in simplest [tex]$a+bi$[/tex] form:

[tex]\sqrt{9}+\sqrt{-36}[/tex]

A. [tex] -9i[/tex]
B. [tex] 3-6i[/tex]
C. [tex] 9i[/tex]
D. [tex] 3+6i[/tex]

Sagot :

GinnyAnswer
To simplify the expression [tex]\(\sqrt{9} + \sqrt{-36}\)[/tex] into the form [tex]\(a + bi\)[/tex], let's break it down step-by-step:

1. Calculate [tex]\(\sqrt{9}\)[/tex]:

[tex]\[ \sqrt{9} = 3 \][/tex]

2. Calculate [tex]\(\sqrt{-36}\)[/tex]:

The square root of a negative number involves an imaginary unit [tex]\(i\)[/tex], where [tex]\(i = \sqrt{-1}\)[/tex]. Thus:

[tex]\[ \sqrt{-36} = \sqrt{36 \cdot (-1)} = \sqrt{36} \cdot \sqrt{-1} = 6i \][/tex]

3. Add the two results together:

[tex]\[ \sqrt{9} + \sqrt{-36} = 3 + 6i \][/tex]

Therefore, the expression [tex]\(\sqrt{9} + \sqrt{-36}\)[/tex] simplifies to:

[tex]\[ \boxed{3 + 6i} \][/tex]
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