Question

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

Answer 1

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

Step-by-step explanation

remember that:

`\begin{gathered} i^2=-1 \\ so \\ √(i^2)=√(-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