Question

Which choice is equivalent to the product below for acceptable values of x? (is my answer right? question below)

Answer 1

Your answer is not correct. As long as the indexes are the same on the radicals, and they are because they are both square roots (as opposed to one being a square root and another being a cubed root, for example) they multiply out exactly the same as they would if there was not a radical sign there. Like this:

Answer 2

\[\sqrt{5x} * \sqrt{x+3}=\sqrt{5x * (x+3)}\]

Answer 3

Distribute the 5x into the parenthesis just like you would with a "regular" expression. That equals...

Answer 4

So, it's A. But then would my answer have to be simplified (the 15) into and 5

Answer 5

3 and 5*

Answer 6

If you factored that again while it is under the radical sign as a single expression, you would end up with what you started with, which is 5x(x+3) all under a single radical...which is fine, but it is not a choice. So you need to leave it with an x^2 in the first term. Distribute the 5x into the (x + 3) and what do you get? 5x(x+3) = ?

Answer 7

Yeah so... it's 5x^2 + 15 (all under the radical of course)

Answer 8

No, its not because you're forgetting that when you multiply the 5x(3) that's 15x not just 15

Answer 9

It's not A

Answer 10

Oh yeah... the x needs to be there. Duh. Then it's C, because when you distribute the 5x the x needs to be there too. :P

Answer 11

Right! Good job!

Answer 12

Thank you so much. :)