Question

How would I write the expression in terms of i and simply

Answer 1

$\sqrt[]{21}\text{ i}$

Explanation

remember that:

$\begin{gathered} i^2=-1 \\ so \\ \sqrt{i^2}=\sqrt{-1} \\ i=\sqrt[]{-1} \end{gathered}$

also

$\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}$

then

Step 1

apply the properties and defiition of i

so

$\begin{gathered} \sqrt[]{-21} \\ \sqrt[]{-21}=\sqrt[]{-1\cdot21} \\ \sqrt[]{-21}=\sqrt[]{-1}\sqrt[]{21} \\ \sqrt[]{-21}=i\sqrt[]{21} \\ \sqrt[]{-21}=\sqrt[]{21}i\text{ } \end{gathered}$

therefore, the answer is

$\sqrt[]{21}\text{ i}$

I hope this helps you