Write the number as the product of a real number and i - √( - 20)

Question

Write the number as the product of a real number and i
`- √( - 20)`

Answer 1

Take into account that 20 = 5*4 = 5*2^2.

Furthermore, -20 = (-1)*20 and i = √-1

Hence, you have:

`-\sqrt[]{20}=-\sqrt[]{(-1)(20)}=-\sqrt[]{(-1)(5\cdot2^2)}=-2\sqrt[]{5}\sqrt[]{-1}=-2\sqrt[]{5}i`

Then answer is -2√5*i