SOLUTION: What is the simpliest form of √ 567w^12

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Question 628188: What is the simpliest form of √ 567w^12
Answer by jim_thompson5910(35256) About Me  (Show Source):
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sqrt%28567%2Aw%5E12%29 Start with the given expression.


sqrt%2881%2A7%2Aw%5E12%29 Factor 567 into 81%2A7


sqrt%2881%2A7%2Aw%5E2%2Aw%5E2%2Aw%5E2%2Aw%5E2%2Aw%5E2%2Aw%5E2%29 Factor w%5E12 into w%5E2%2Aw%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 81 to get 9.


9%2Asqrt%287%29%2Aw%2Aw%2Aw%2Aw%2Aw%2Aw Take the square root of w%5E2 to get w.


9w%5E6%2Asqrt%287%29 Rearrange and multiply the terms.

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Answer:


So sqrt%28567%2Aw%5E12%29 simplifies to 9w%5E6%2Asqrt%287%29


In other words, sqrt%28567%2Aw%5E12%29=9w%5E6%2Asqrt%287%29 where 'w' is non-negative.

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