Express the radical using the imaginary unit, $i$ . $\newline$ Express your answer in simplified form. $\newline$ $\pm \sqrt{-20}= \pm \square$

Full solution

Q. Express the radical using the imaginary unit,

i

\newline

Express your answer in simplified form.

\newline

\pm \sqrt{-20}= \pm \square

Rephrasing and recognizing: First, let's rephrase the ＂Express the radical using the imaginary unit, $i$ , and simplify the expression $\pm\sqrt{-20}$ .＂
Separating the square root: Recognize that the square root of a negative number involves the imaginary unit $i$ , where $i^2 = -1$ . We can express $\pm\sqrt{-20}$ as $\pm\sqrt{-1 \times 20}$ .
Replacing $\sqrt{-1}$ with $i$ : Separate the square root of the product into the product of square roots, knowing that $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ . This gives us $\pm\sqrt{-1} \cdot \sqrt{20}$ .
Simplifying $\sqrt{20}$ : Replace $\sqrt{-1}$ with $i$ , since they are equivalent. This transforms the expression into $\pm i \cdot \sqrt{20}$ .
Taking the square root of $4$ : Simplify $\sqrt{20}$ by factoring it into $\sqrt{4 \times 5}$ , since $4$ is a perfect square and its square root can be easily calculated.
Combining constants outside the radical: Take the square root of $4$ , which is $2$ , and bring it outside the radical. This leaves us with $\pm i \cdot 2 \cdot \sqrt{5}$ .
Combining constants outside the radical: Take the square root of $4$ , which is $2$ , and bring it outside the radical. This leaves us with $\pm i \cdot 2 \cdot \sqrt{5}$ .Combine the constants outside the radical to simplify the expression. This results in $\pm 2i \cdot \sqrt{5}$ .