SOLUTION: Hello, I need help with my math homework please. What is square root sign 162 x to the fifth "162x5" in a square root sign?

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Question 604334: Hello, I need help with my math homework please. What is square root sign 162 x to the fifth "162x5" in a square root sign?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28162%2Ax%5E5%29 Start with the given expression.


sqrt%2881%2A2%2Ax%5E5%29 Factor 162 into 81%2A2


sqrt%2881%2A2%2Ax%5E2%2Ax%5E2%2Ax%29 Factor x%5E5 into x%5E2%2Ax%5E2%2Ax


sqrt%2881%29%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


9%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29 Take the square root of 81 to get 9.


9%2Asqrt%282%29%2Ax%2Ax%2Asqrt%28x%29 Take the square root of x%5E2 to get x.


9x%5E2%2Asqrt%282x%29 Rearrange and multiply the terms.

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Answer:


So sqrt%28162%2Ax%5E5%29 simplifies to 9x%5E2%2Asqrt%282x%29


In other words, sqrt%28162%2Ax%5E5%29=9x%5E2%2Asqrt%282x%29 where x is non-negative.