SOLUTION: How do you find the square root of 75x3y5?

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Question 194062: How do you find the square root of 75x3y5?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt%2875%2Ax%5E3%2Ay%5E5%29 Start with the given expression.


sqrt%2825%2A3%2Ax%5E3%2Ay%5E5%29 Factor 75 into 25%2A3


sqrt%2825%2A3%2Ax%5E2%2Ax%2Ay%5E5%29 Factor x%5E3 into x%5E2%2Ax


sqrt%2825%2A3%2Ax%5E2%2Ax%2Ay%5E2%2Ay%5E2%2Ay%29 Factor y%5E5 into y%5E2%2Ay%5E2%2Ay


Break up the square root using the identity sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29.


Take the square root of 25 to get 5.


5%2Asqrt%283%29%2Ax%2Asqrt%28x%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28y%29 Take the square root of x%5E2 to get x.


5%2Asqrt%283%29%2Ax%2Asqrt%28x%29%2Ay%2Ay%2Asqrt%28y%29 Take the square root of y%5E2 to get y.


5xy%5E2%2Asqrt%283xy%29 Rearrange and combine the terms.

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Answer:


So sqrt%2875%2Ax%5E3%2Ay%5E5%29 simplifies to 5xy%5E2%2Asqrt%283xy%29


In other words, sqrt%2875%2Ax%5E3%2Ay%5E5%29=5xy%5E2%2Asqrt%283xy%29 where every variable is non-negative.