Question

How do you simplify `sqrt(-50)`?

Answer 1

I found: `sqrt(-50)=5isqrt(2)`

Explanation:

Here you have a problem...
in fact you cannot solve a square root with a negative argument or, better, you cannot find a real number which is solution of your square root.

What you can do it is try to find a solution somewhere else...in the place of imaginary numbers!
First of all you manipulate your root as:
`sqrt(-50)=sqrt(-1*2*25)=sqrt(-1)sqrt(25)sqrt(2)=5sqrt(-1)sqrt(2)`
you now introduce a new entity: the imaginary unit `i` given as:
`i=sqrt(-1)`
so you can write:
`sqrt(-50)=5isqrt(2)` which is:

1] solution of your problem; in fact if you square it you get:
`(5isqrt(2))^2=25*-1*2=-50` that is your original radicand!

2] it is an imaginary number (it contains `i`).