SOLUTION: Please help me. Simplify. Assume that all variables represent positive real numbers. The square root of 3wy^3 times the sqaure root of 12w^2 y Thanks!

Algebra ->  Square-cubic-other-roots -> SOLUTION: Please help me. Simplify. Assume that all variables represent positive real numbers. The square root of 3wy^3 times the sqaure root of 12w^2 y Thanks!      Log On


   

Question 190644: Please help me.
Simplify. Assume that all variables represent positive real numbers.
The square root of 3wy^3 times the sqaure root of 12w^2 y
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%283wy%5E3%29%2Asqrt%2812w%5E2y%29 Start with the given expression.


sqrt%28%283wy%5E3%29%2812w%5E2y%29%29 Combine the roots using the identity sqrt%28A%29%2Asqrt%28B%29=sqrt%28A%2AB%29


sqrt%28%283%2A12%29%28wy%5E3%2Aw%5E2y%29%29 Rearrange the terms.


sqrt%2836wy%5E3%2Aw%5E2y%29 Multiply 3 and 12 to get 36


sqrt%2836w%5E%281%2B2%29y%5E%283%2B1%29%29 Multiply the variable terms by adding the corresponding exponents.


sqrt%2836w%5E3y%5E4%29 Add


sqrt%2836%2Aw%5E2%2Aw%2Ay%5E4%29 Factor w%5E3 into w%5E2%2Aw


sqrt%2836%2Aw%5E2%2Aw%2Ay%5E2%2Ay%5E2%29 Factor y%5E4 into y%5E2%2Ay%5E2


sqrt%2836%29%2Asqrt%28w%5E2%29%2Asqrt%28w%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


6%2Asqrt%28w%5E2%29%2Asqrt%28w%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 Take the square root of 36 to get 6.


6%2Aw%2Asqrt%28w%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 Take the square root of w%5E2 to get w.


6%2Aw%2Asqrt%28w%29%2Ay%2Ay Take the square root of y%5E2 to get y.


6wy%5E2%2Asqrt%28w%29 Rearrange and multiply.

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Answer:


So sqrt%283wy%5E3%29%2Asqrt%2812w%5E2y%29 simplifies to 6wy%5E2%2Asqrt%28w%29


In other words, sqrt%283wy%5E3%29%2Asqrt%2812w%5E2y%29=6wy%5E2%2Asqrt%28w%29 where every variable is non-negative.