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

Dec 2019
8
0
Windsor Ontario Canada
I'm not sure what the result of sqrt (h^2+15) * sqrt (h+15) turns into image1.jpeg
 

topsquark

Math Team
May 2013
2,442
1,012
The Astral plane
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
 
  • Like
Reactions: idontknow

romsek

Math Team
Sep 2015
2,872
1,607
USA
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$
 
  • Like
Reactions: topsquark
Dec 2019
8
0
Windsor Ontario Canada
@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.
 
Dec 2019
8
0
Windsor Ontario Canada
@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
May 2013
2,442
1,012
The Astral plane
@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