SOLUTION: I am unsure how to solve this problem: z sqrt 50zu^2- 8u sqrt 2z^3 Thank you for your help

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Question 177297: I am unsure how to solve this problem:
z sqrt 50zu^2- 8u sqrt 2z^3
Thank you for your help

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, simplify sqrt%2850zu%5E2%29

sqrt%2850%2Az%2Au%5E2%29 Start with the given expression.


sqrt%2825%2A2%2Az%2Au%5E2%29 Factor 50 into 25%2A2


sqrt%2825%29%2Asqrt%282%29%2Asqrt%28z%29%2Asqrt%28u%5E2%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


5%2Asqrt%282%29%2Asqrt%28z%29%2Asqrt%28u%5E2%29 Take the square root of 25 to get 5.


5%2Asqrt%282%29%2Asqrt%28z%29%2Au Take the square root of u%5E2 to get u.


5u%2Asqrt%282z%29 Rearrange and combine the terms.



So sqrt%2850%2Az%2Au%5E2%29=5u%2Asqrt%282z%29 where every variable is positive.


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Now let's simplify sqrt%282%2Az%5E3%29


sqrt%282%2Az%5E3%29 Start with the given expression.


sqrt%282%2Az%5E2%2Az%29 Factor z%5E3 into z%5E2%2Az


sqrt%282%29%2Asqrt%28z%5E2%29%2Asqrt%28z%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


sqrt%282%29%2Az%2Asqrt%28z%29 Take the square root of z%5E2 to get z.


z%2Asqrt%282z%29 Rearrange and combine the terms.


So sqrt%282%2Az%5E3%29=z%2Asqrt%282z%29 where every variable is positive.



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So


z%2Asqrt%2850zu%5E2%29-8u%2Asqrt%282%2Az%5E3%29


simplifies to


z%2A5u%2Asqrt%282z%29-8u%2Az%2Asqrt%282z%29



5uz%2Asqrt%282z%29-8uz%2Asqrt%282z%29 Rearrange the terms.


sqrt%282z%29%2A%285uz-8uz%29 Factor out sqrt%282z%29


sqrt%282z%29%2A%28-3uz%29 Combine like terms.


-3uz%2Asqrt%282z%29 Rearrange the terms.



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Answer:

So z%2Asqrt%2850zu%5E2%29-8u%2Asqrt%282%2Az%5E3%29 completely simplifies to -3uz%2Asqrt%282z%29



In other words, z%2Asqrt%2850zu%5E2%29-8u%2Asqrt%282%2Az%5E3%29=-3uz%2Asqrt%282z%29 where every variable is positive.