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Express the radical using the imaginary unit, i.
Express your answer in simplified form.
Sqrt-14

Sagot :

AlgebraicAardvark

The foundation of imaginary numbers is that [tex]i = \sqrt{-1}[/tex].

When simplifying radicals involving square roots of negative numbers, your first step is to separate the negative from the number and turn it into [tex]i[/tex].

    [tex]\begin{aligned}\sqrt{-14} &= \sqrt{-1 \cdot 14}\\[0.5em] &= \sqrt{-1 }\cdot \sqrt{14}\\[0.5em] &= i\cdot \sqrt{14}\end{aligned}[/tex]

At this point, you can turn to the [tex]\sqrt{14}[/tex] and decide if this can be simplified or not.  (Ask youself if there are any perfect squares that divide into 14.)

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