Write sqrt(-125) in simplest radical form. Answer:

Split into Product: Express sqrt(-125) as the product of square roots and sqrt(-1). sqrt(-125) = sqrt(-1 * 125) = sqrt(-1) * sqrt(125)Express as Complex Number: Express sqrt(-1) * sqrt(125) as a complex number by using i. sqrt(-125) = sqrt(-1) * sqrt(125) = i * sqrt(125)Factor and Simplify: Simplify sqrt(125) by factoring it into sqrt(25 * 5). sqrt(125) = sqrt(25 * 5) = sqrt(25) * sqrt(5) = 5 * sqrt(5)Combine Results: Combine the results to express sqrt(-125) in simplest radical form. sqrt(-125) = i * 5 * sqrt(5) = 5i * sqrt(5)

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Write
sqrt(-125) in simplest radical form.
Answer:

Write $\sqrt{-125}$ in simplest radical form. $\newline$ Answer:

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Math Problems

Algebra 2

Introduction to complex numbers

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Q. Write

\sqrt{-125}

in simplest radical form.

\newline

Answer:

Split into Product: Express $\sqrt{-125}$ as the product of square roots and $\sqrt{-1}$ . $\sqrt{-125} = \sqrt{-1 \times 125} = \sqrt{-1} \times \sqrt{125}$
Express as Complex Number: Express $\sqrt{-1} \times \sqrt{125}$ as a complex number by using $i$ . $\sqrt{-125} = \sqrt{-1} \times \sqrt{125} = i \times \sqrt{125}$
Factor and Simplify: Simplify $\sqrt{125}$ by factoring it into $\sqrt{25 \times 5}$ . $\sqrt{125} = \sqrt{25 \times 5} = \sqrt{25} \times \sqrt{5} = 5 \times \sqrt{5}$
Combine Results: Combine the results to express $\sqrt{-125}$ in simplest radical form. $\sqrt{-125} = i \times 5 \times \sqrt{5} = 5i \times \sqrt{5}$