SOLUTION: Simplify 4√16x^3y^2 -5y√4x^3 Thank you.

Algebra ->  Algebra  -> Radicals -> SOLUTION: Simplify 4√16x^3y^2 -5y√4x^3 Thank you.      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 176405: Simplify 4√16x^3y^2 -5y√4x^3 Thank you.
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
To simplify this expression, we need to simplify the individual radicals.

Let's simplify sqrt%2816x%5E3y%5E2%29


sqrt%2816x%5E3y%5E2%29 Start with the given expression.


sqrt%2816x%5E2%2Ax%2Ay%5E2%29 Factor x%5E3 to get x%5E2%2Ax


sqrt%2816%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 Break up the square root.


4%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 Take the square root of 16 to get 4


4%2Ax%2Asqrt%28x%29%2Asqrt%28y%5E2%29 Take the square root of x%5E2 to get x


4%2Ax%2Asqrt%28x%29%2Ay Take the square root of y%5E2 to get y


4xy%2Asqrt%28x%29 Rearrange the terms.


So sqrt%2816x%5E3y%5E2%29=4xy%2Asqrt%28x%29 where every variable is positive.


============================================================


Now let's simplify sqrt%284x%5E3%29


sqrt%284x%5E3%29 Start with the given expression.


sqrt%284x%5E2%2Ax%29 Factor x%5E3 to get x%5E2%2Ax


sqrt%284%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29 Break up the square root.


2%2Asqrt%28x%5E2%29%2Asqrt%28x%29 Take the square root of 4 to get 2


2x%2Asqrt%28x%29 Take the square root of x%5E2 to get x


So sqrt%284x%5E3%29=2x%2Asqrt%28x%29 where "x" is positive.



===========================================================


Since sqrt%2816x%5E3y%5E2%29=4xy%2Asqrt%28x%29 and sqrt%284x%5E3%29=2x%2Asqrt%28x%29 (where every variable is positive), this means that


4%2Asqrt%2816x%5E3y%5E2%29-5y%2Asqrt%284x%5E3%29


simplifies to


4%2A%284xy%2Asqrt%28x%29%29-5y%2A%282x%2Asqrt%28x%29%29


16xy%2Asqrt%28x%29-5y%2A%282x%2Asqrt%28x%29%29 Multiply 4 and 4xy to get 16xy


16xy%2Asqrt%28x%29-10xy%2Asqrt%28x%29 Multiply 5y and 2x to get 10xy


sqrt%28x%29%2A%2816xy-10xy%29 Factor out the GCF sqrt%28x%29


sqrt%28x%29%2A%286xy%29 Combine like terms


6xy%2Asqrt%28x%29 Rearrange the terms



=================================================================


Answer:


So 4%2Asqrt%2816x%5E3y%5E2%29-5y%2Asqrt%284x%5E3%29=6xy%2Asqrt%28x%29 where every variable is positive.