what is the square root of -36 i dont understand why the calculator said 6i

Think about this......what real number could we multiply by itself to get -36 ???

Answer.....there isn't any.....a positive times a positive is a positive......and a negative times a negative is a positive

Now......let's define an imaginary number, i,  to be √-1

So

√-36 = √[-1 * 36] = √-1 * √36 =  i * 6   = 6i

And that's why your calculator gave you that answer.....

i stands for imaginary number, $${i} = {\sqrt{-{\mathtt{1}}}}$$.

this is because no number squared can equal a negative number

$${\left(-{\mathtt{1}}\right)}^{{\mathtt{2}}} = \left(-{\mathtt{1}}\right){\mathtt{\,\times\,}}\left(-{\mathtt{1}}\right)$$

a negative times a negative is a positive so the answer is just 1
positive times positive is also positive so you get 1.

if a math problem asked you for the square root of a negative number you either learned about it already or somewhere else you made a mistake.

good luck yo