SOLUTION: Please put in simplest form sqrt75y^4w^3

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Question 303462: Please put in simplest form
sqrt75y^4w^3
Found 2 solutions by jim_thompson5910, mananth:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2875%2Ay%5E4%2Aw%5E3%29 Start with the given expression.


sqrt%2825%2A3%2Ay%5E4%2Aw%5E3%29 Factor 75 into 25%2A3


sqrt%2825%2A3%2Ay%5E2%2Ay%5E2%2Aw%5E3%29 Factor y%5E4 into y%5E2%2Ay%5E2


sqrt%2825%2A3%2Ay%5E2%2Ay%5E2%2Aw%5E2%2Aw%29 Factor w%5E3 into w%5E2%2Aw


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


5%2Asqrt%283%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28w%5E2%29%2Asqrt%28w%29 Take the square root of 25 to get 5.


5%2Asqrt%283%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Aw%2Asqrt%28w%29 Take the square root of w%5E2 to get w.


5%2Asqrt%283%29%2Ay%2Ay%2Aw%2Asqrt%28w%29 Take the square root of y%5E2 to get y.


5wy%5E2%2Asqrt%283w%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2875%2Ay%5E4%2Aw%5E3%29 simplifies to 5wy%5E2%2Asqrt%283w%29


In other words, sqrt%2875%2Ay%5E4%2Aw%5E3%29=5wy%5E2%2Asqrt%283w%29 where every variable is non-negative.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt75y^4w^3
sqrt (5*5*3y^4 *w*w*w)
5*y^2*wsqrt(3*w)
5y^2wsqrt3w