SOLUTION: Simplify (2x^3 /(sqaure root of x^3 + 4)) + (5(square root of x^3 + 4)) I just don't know what to do with the square roots when trying to simply Thanks Tiffany P.S. Sorry

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify (2x^3 /(sqaure root of x^3 + 4)) + (5(square root of x^3 + 4)) I just don't know what to do with the square roots when trying to simply Thanks Tiffany P.S. Sorry       Log On


   

Question 24272: Simplify
(2x^3 /(sqaure root of x^3 + 4)) + (5(square root of x^3 + 4))
I just don't know what to do with the square roots when trying to simply
Thanks
Tiffany
P.S. Sorry I didn't know how to type a sqaure root sign so I just wrote it
Answer by kev82(151) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
This is actually a really easy fractions problem, hidden behind some horrible looking algebra. All you have to do is remember how to add fractions. Let's try a simple example:
1%2F5+%2B+2%2F7
We need to work out a common denominator for ecah of the fractions. A common denomitator, is just a common multiple of 5 and 7. The most obvious choice is 35. Now we rewite the fractions:
1%2F5=7%2F35 and 2%2F7=10%2F35
Now we add them giving %287%2B10%29%2F35=17%2F35
Doing the same thing with your problem we have
%282x%5E3%29%2Fsqrt%28x%5E3%2B4%29%2B5%2Asqrt%28x%5E3%2B4%29%2F1
Taking sqrt%28x%5E3%2B4%29 as the common denominator, we rewrite the problem as

But notice that sqrt%28x%5E3%2B4%29%2Asqrt%28x%5E3%2B4%29=sqrt%28x%5E3%2B4%29%5E2 which is just x%5E3%2B4
Using this, and adding the fractions, we get
%282%2Ax%5E3%2B5%2A%28x%5E3%2B4%29%29%2Fsqrt%28x%5E3%2B4%29
I'm sure you can tidy that up to get an answer of
%287x%5E3%2B20%29%2Fsqrt%28x%5E3%2B4%29
At university level you would be expected to either show the fraction is in it's lowest form, or cancel it to it's lowest form. But factoring cubics is probably too hard for schoolwork, so I'll just tell you that this is as simplified as it gets.
Hope that helps
Kev