SOLUTION: Can you please explain to me how to simplify the following equation? {{{sqrt 32x^4y^2}}} thank you.

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Question 201751: Can you please explain to me how to simplify the following equation?

sqrt+32x%5E4y%5E2
thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: you need to enclose "32x^4y^2" in parenthesis to go from sqrt+32x%5E4y%5E2 to sqrt%2832%2Ax%5E4%2Ay%5E2%29



sqrt%2832%2Ax%5E4%2Ay%5E2%29 Start with the given expression.


sqrt%2816%2A2%2Ax%5E4%2Ay%5E2%29 Factor 32 into 16%2A2


sqrt%2816%2A2%2Ax%5E2%2Ax%5E2%2Ay%5E2%29 Factor x%5E4 into x%5E2%2Ax%5E2


sqrt%2816%29%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28y%5E2%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


4%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28y%5E2%29 Take the square root of 16 to get 4.


4%2Asqrt%282%29%2Ax%2Ax%2Asqrt%28y%5E2%29 Take the square root of x%5E2 to get x.


4%2Asqrt%282%29%2Ax%2Ax%2Ay Take the square root of y%5E2 to get y.


4x%5E2y%2Asqrt%282%29 Rearrange and multiply the terms.

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Answer:


So sqrt%2832%2Ax%5E4%2Ay%5E2%29 simplifies to 4x%5E2y%2Asqrt%282%29


In other words, sqrt%2832%2Ax%5E4%2Ay%5E2%29=4x%5E2y%2Asqrt%282%29 where every variable is non-negative.


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