square root of (9+4x) x square root of (9+4x) =?

Question

anonymous · Answer

Is that "x" in the middle a symbol for multiplication? Like this? : $$\sqrt{9+4x} * \sqrt{9+4x}$$

anonymous · Answer

yes!

anonymous · Answer

I was tempted to foil.., but then I think I also am tempted to make it 9 + 4x.

anonymous · Answer

When you are multiplying the square root of the exact same thing, the square root disappears. You are multiplying two exact same quantities together, so something times the same something = (something) squared.$$\sqrt{9+4x} * \sqrt{9+4x} = (\sqrt{9+4x})^{2}$$ If you have a square root to the power of 2, that power of 2 makes the square root go away. So you are just left with 9+4x.

anonymous · Answer

Ah alright thanks!!! :)

anonymous · Answer

Do you know why a power of 2 makes a square root go away? Because a square root just means "the power of 1/2." So a square root of something means that something to the power of 1/2. $$\sqrt{9+4x}=(9+4x)^{1/2}$$
Now to square that, we have:$$((9+4x)^{1/2})^{2}$$
Multiplying those exponents gives 1/2 * 2, which is just equal to 1. So (9+4x) to the power of 1 is just itself, (9+4x).

Just a side note ;) You're welcome!

anonymous · Answer

Ah, this makes a lot of sense. Thanks so much!