Question 812624
First of all, please try to post your questions under appropriate categories. This problem has nothing to do with conic sections. I have changed the category to a more appropriate one.<br>
{{{sqrt(-27)*sqrt(-50)}}}
With negative radicands in square roots we are working with complex numbers. ("Radicand" is the name for the expression that appears inside a radical.) It is important to recognize the presence of complex numbers because it will dictate the proper procedure.<br>
When working with complex numbers it is important to rewrite the expression in terms of "i" (which is defined as {{{sqrt(-1)}}}) before doing anything else:
{{{sqrt(-1*27)*sqrt(-1*50)}}}
{{{sqrt(-1)*sqrt(27)*sqrt(-1)*sqrt(50)}}}
{{{i*sqrt(27)*i*sqrt(50)}}}<br>
Now we can simplify the remaining square roots and then multiply or we can do it the other way around. Since I don't feel like multiplying 27 and 50 I choose to simplify first:
{{{i*sqrt(9*3)*i*sqrt(25*2)}}}
{{{i*sqrt(9)*sqrt(3)*i*sqrt(25)*sqrt(2)}}}
{{{i*3*sqrt(3)*i*5*sqrt(2)}}}
Now we multiply:
{{{15i^2*sqrt(3*2)}}}
{{{15(-1)*sqrt(6)}}}   Since {{{i^2 = -1}}}
{{{-15*sqrt(6)}}}
This is the simplified result.