SOLUTION: Simplify the square root. Do not assume variables represent positive numbers. Square root of 18x^3y^2

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Question 761663: Simplify the square root. Do not assume variables represent positive numbers.
Square root of 18x^3y^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2818%2Ax%5E3%2Ay%5E2%29 Start with the given expression.


sqrt%289%2A2%2Ax%5E3%2Ay%5E2%29 Factor 18 into 9%2A2


sqrt%289%2A2%2Ax%5E2%2Ax%2Ay%5E2%29 Factor x%5E3 into x%5E2%2Ax


sqrt%289%29%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


3%2Asqrt%282%29%2Asqrt%28x%5E2%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 Take the square root of 9 to get 3.


3%2Asqrt%282%29%2Aabs%28x%29%2Asqrt%28x%29%2Asqrt%28y%5E2%29 Take the square root of x%5E2 to get abs%28x%29.


3%2Asqrt%282%29%2Aabs%28x%29%2Asqrt%28x%29%2Aabs%28y%29 Take the square root of y%5E2 to get abs%28y%29.


3%2Aabs%28x%29%2Aabs%28y%29%2Asqrt%282x%29 Rearrange and multiply the terms.


3%2Aabs%28x%2Ay%29%2Asqrt%282x%29 Combine the absolute values.

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Answer:


So sqrt%2818%2Ax%5E3%2Ay%5E2%29 simplifies to 3%2Aabs%28x%2Ay%29%2Asqrt%282x%29


In other words, sqrt%2818%2Ax%5E3%2Ay%5E2%29=3%2Aabs%28x%2Ay%29%2Asqrt%282x%29