Question

Complex numbers simplify √72

Answer 1

We have the complex number:

`\sqrt[]{-72}`

And we want to simplify, so we need to factorize the number -72:

`\begin{gathered} \sqrt[]{-72}=\sqrt[]{(-1)\cdot72}=(\sqrt[]{72})i=(\sqrt[]{2\cdot36})i=\sqrt[]{36}\sqrt[]{2}\cdot i=6\cdot\sqrt[]{2}\cdot i \\ So\colon \\ \sqrt[]{-72}=6\cdot\sqrt[]{2}\cdot i \\ \text{Note that }\sqrt[]{(-1)}=i \end{gathered}`