Stuck on a simplification sqrt h^2+15 * sqrt h+15

JamesM0025

I'm not sure what the result of sqrt (h^2+15) * sqrt (h+15) turns into

topsquark

Math Team
For any a, b real we have that $$\displaystyle (a + b)(a - b) = a^2 - b^2$$.

In your case you have $$\displaystyle a = \sqrt{h^2 + 15}$$ and $$\displaystyle b = \sqrt{h + 15}$$.

So what is $$\displaystyle a^2 - b^2$$?

-Dan

idontknow

romsek

Math Team
Are you sure you're not just supposed to use L'Hopital's rule?

$\lim \limits_{h\to 1} \dfrac{\dfrac{h}{\sqrt{h^2+15}} - \dfrac{1}{2\sqrt{h+15}}}{\dfrac{1}{2\sqrt{h+3}}} = \\~\\ \dfrac{\dfrac 1 4 - \dfrac 1 8}{\dfrac 1 4} = \dfrac 4 8 = \dfrac 1 2$

topsquark

JamesM0025

@topsquark thanks for the help but i found myself getting lost in the expanded form of it. Which just added to my confusion when i ended up with 128 but the answer is 1/2 lol. If you scroll up you can see the original question if you have the time.

JamesM0025

@romsek Its a review for a midterm on saturday, but I know in our latest lab when solving limits it said to not use that rule, so it might also be a thing on the midterm .. or maybe it wont be. I've never seen that rule before ill have to watch a video

topsquark

Math Team
@topsquark thanks for the help but i found myself getting lost in the expanded form of it. Which just added to my confusion when i ended up with 128 but the answer is 1/2 lol. If you scroll up you can see the original question if you have the time.
I don't understand. I looked at the original and you had left it in the form (a + b)(a - b). The numerator comes out to be $$\displaystyle (h^2 + 15) - (h + 15) = h^2 - h$$.

-Dan