SOLUTION: Can you please answer this problem? square root of (128x^5y^3)

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Question 190506: Can you please answer this problem? square root of (128x^5y^3)
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%28128%2Ax%5E5%2Ay%5E3%29 Start with the given expression.


sqrt%2864%2A2%2Ax%5E5%2Ay%5E3%29 Factor 128 into 64%2A2


sqrt%2864%2A2%2Ax%5E2%2Ax%5E2%2Ax%2Ay%5E3%29 Factor x%5E5 into x%5E2%2Ax%5E2%2Ax


sqrt%2864%2A2%2Ax%5E2%2Ax%5E2%2Ax%2Ay%5E2%2Ay%29 Factor y%5E3 into y%5E2%2Ay


sqrt%2864%29%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


8%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29 Take the square root of 64 to get 8.


8%2Asqrt%282%29%2Ax%2Ax%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29 Take the square root of x%5E2 to get x.


8%2Asqrt%282%29%2Ax%2Ax%2Asqrt%28x%29%2Ay%2Asqrt%28y%29 Take the square root of y%5E2 to get y.


8x%5E2y%2Asqrt%282xy%29 Rearrange and multiply.

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Answer:


So sqrt%28128%2Ax%5E5%2Ay%5E3%29 simplifies to 8x%5E2y%2Asqrt%282xy%29


In other words, sqrt%28128%2Ax%5E5%2Ay%5E3%29=8x%5E2y%2Asqrt%282xy%29 where every variable is non-negative.