SOLUTION: √(12w^4 ) Rewrite the following in simplified radical form, assume that all variables represent positive real numbers

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Question 295600: √(12w^4 ) Rewrite the following in simplified radical form, assume that all variables represent positive real numbers


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2812%2Aw%5E4%29 Start with the given expression.


sqrt%284%2A3%2Aw%5E4%29 Factor 12 into 4%2A3


sqrt%284%2A3%2Aw%5E2%2Aw%5E2%29 Factor w%5E4 into w%5E2%2Aw%5E2


sqrt%284%29%2Asqrt%283%29%2Asqrt%28w%5E2%29%2Asqrt%28w%5E2%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


2%2Asqrt%283%29%2Asqrt%28w%5E2%29%2Asqrt%28w%5E2%29 Take the square root of 4 to get 2.


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


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

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Answer:


So sqrt%2812%2Aw%5E4%29 simplifies to 2w%5E2%2Asqrt%283%29


In other words, sqrt%2812%2Aw%5E4%29=2w%5E2%2Asqrt%283%29 where w%3E=0