Brainlet here. Is there an intuitive way of looking at this?

>>8814585
sqrt(-4)sqrt(-9) = ?

>>8814585
[math](xy)^{0.5} = x^{0.5}y^{0.5}[/math]

try thinking about it geometrically

>>8814585
Look at the definition of a square root, then apply your knowledge of arithmetics.

>>8814585
Distributive property of exponents as shown by:
>>8814601 et al.
But as you are a massive brainlet, let me try write something up for you:
sqr(x) just 'asks the question' "what number multiplied by itself yields x." So, if we have sqr(xy) "What number multiplied by itself yields xy?" Naturally, this is then the product of the number which needs to be multiplied by itself to give x and the number which needs to be multiplied by itself to give y. So sqr(x)*sqr(y)

>>8814628
Ignore my autism. Hopefully it works this time.
[eqn](\sqrt{x}\sqrt{y})^2=(\sqrt{x}\sqrt{y})(\sqrt{x}\sqrt{y})=\sqrt{x}\sqrt{x}\sqrt{y}\sqrt{y}=xy[/eqn]then[eqn](\sqrt{x}\sqrt{y})^2=xy[/eqn]so that[eqn]\sqrt{x}\sqrt{y}=\sqrt{xy}[/eqn]

>>8814635
Another viewpoint that might make it easier for you:
you know that sqr(x^2)=x right?
So then sqr(x^2)=sqr(x*x)=sqr(x)*sqr(x)=x
If we have x and y we just can't simplify it to x.

>>8814593
6

>>8814639
lol

>>8815027
sqrt(-9)
= sqrt(-1) * sqrt(9)
= i * 3

sqrt(-4)
= sqrt(-1) * sqrt(4)
= i * 2

sqrt(-4) * sqrt(-9)
= (i * 3) * (i * 2)
= i^2 * 3 * 2
= -1 * 6
= -6