SOLUTION: sqrt of 12x to the 7th power x w to the 10th power

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Question 388546: sqrt of 12x to the 7th power x w to the 10th power
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2812%2Ax%5E7%2Aw%5E10%29 Start with the given expression.


sqrt%284%2A3%2Ax%5E7%2Aw%5E10%29 Factor 12 into 4%2A3


sqrt%284%2A3%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%2Aw%5E10%29 Factor x%5E7 into x%5E2%2Ax%5E2%2Ax%5E2%2Ax


sqrt%284%2A3%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%2Aw%5E2%2Aw%5E2%2Aw%5E2%2Aw%5E2%2Aw%5E2%29 Factor w%5E10 into w%5E2%2Aw%5E2%2Aw%5E2%2Aw%5E2%2Aw%5E2


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


Take the square root of 4 to get 2.


Take the square root of w%5E2 to get w.


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


2w%5E5x%5E3%2Asqrt%283x%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2812%2Ax%5E7%2Aw%5E10%29 simplifies to 2w%5E5x%5E3%2Asqrt%283x%29


In other words, sqrt%2812%2Ax%5E7%2Aw%5E10%29=2w%5E5x%5E3%2Asqrt%283x%29 where every variable is non-negative.