Question

-sqrt-50 in radical form

Answer 1

We have the following expression:

`-\sqrt[]{-50}`

The prime factorization of 50 is

`\begin{gathered} 50=2*5*5 \\ 50=2*5^2 \end{gathered}`

Then, we can rewritte our expression as

`-\sqrt[]{-50}=-\sqrt[]{-(2*5^2})=-i\sqrt[]{2*5^2}`

because the square root of -1 is defined as the complex i. Then, we have

`\begin{gathered} -\sqrt[]{-50}=-i*\sqrt[]{2}*\sqrt[]{5^2} \\ or\text{ equivalently,} \\ -\sqrt[]{-50}=-i*\sqrt[]{2}*5 \end{gathered}`

Therefore, the answer is

`-\sqrt[]{-50}=-5\sqrt[]{2}\text{ i}`