Question

-sqrt-50 in radical form

Answer 1

We have the following expression:

$-\sqrt[]{-50}$

The prime factorization of 50 is

$\begin{gathered} 50=2\times5\times5 \\ 50=2\times5^2 \end{gathered}$

Then, we can rewritte our expression as

$-\sqrt[]{-50}=-\sqrt[]{-(2\times5^2})=-i\sqrt[]{2\times5^2}$

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

$\begin{gathered} -\sqrt[]{-50}=-i\times\sqrt[]{2}\times\sqrt[]{5^2} \\ or\text{ equivalently,} \\ -\sqrt[]{-50}=-i\times\sqrt[]{2}\times5 \end{gathered}$

Therefore, the answer is

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