# How do you perform the operation and write the result in standard form given #sqrt(-75)^2#?

##### 1 Answer

Nov 22, 2016

#### Explanation:

Here's another way of looking at this question:

If it exists, then

So, provided it exists,

There is no Real number which will result in a negative number when squared, so

In general, if

#sqrt(n) = i sqrt(-n)#

This is certainly *a* square root of

#(i sqrt(-n))^2 = i^2 * (sqrt(-n))^2 = (-1) * (-n) = n#

The other square root of

In our particular example, we find:

#(sqrt(-75))^2 = (i sqrt(75))^2 = i^2(sqrt(75))^2 = -1*75 = -75#