Question

Hi I need help with this question, please and thank you

Answer 1

We have the following number, we need to simplify:

`6\cdot\sqrt[]{-2401}`

we can also express this as:

`\begin{gathered} 6\cdot\sqrt[]{(-1)\cdot(2401)} \\ 6\sqrt[]{(-1)\cdot(49)\cdot(49)} \end{gathered}`
`\begin{gathered} =6\sqrt[]{-1\cdot49^2} \\ =6\cdot\sqrt[]{-1}\cdot\sqrt[]{49^2} \\ =6\cdot\sqrt[]{-1}\cdot49 \\ =6\cdot49\cdot\sqrt[]{-1} \end{gathered}`

since:

`\sqrt[]{-1}=i`

which represents the imaginary number,

then, we get:

`6\sqrt[]{-2401}=6\cdot49\cdot i=294i`