Question

You are finding the product of two square roots. Each radicand is the same variable raised to an odd power. Explain why you would want to multiply the radicands together first and then simplify the product. Im pretty sure you do this to find a common factor. am I right?

Answer 1

Close, but not quite.
Consider that\[\sqrt(a)*\sqrt(b) = \sqrt(a*b)\]and that\[a^x * a^y = a ^{x+y}\]So then\[\sqrt(a^x)*\sqrt(a^y) = \sqrt(a^{x+y}) = a^{(x+y)/2}\]But if x and y are both odd, then x+y is even, so x+y/2 is a nice round number.

Answer 2

thanks