SOLUTION: How do you factor the square root of 252x^3y^4? I have a bunch of problems like this, this is just the first one. I have asked several people for help but we are all stumped. I wo

Algebra ->  Square-cubic-other-roots -> SOLUTION: How do you factor the square root of 252x^3y^4? I have a bunch of problems like this, this is just the first one. I have asked several people for help but we are all stumped. I wo      Log On


   



Question 552582: How do you factor the square root of 252x^3y^4? I have a bunch of problems like this, this is just the first one. I have asked several people for help but we are all stumped. I would very much appreciate a simple explanation of how to do this.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You take each factor and do a sqrt on it. Sometimes the factor ae perfect squares, but most times they are not. Many times the factors include something that IS a perfect square. So let's do the problem you noted in a detailed step by step way. Once you see the method, you will be able to skip some of the steps
sqrt%28252x%5E3y%5E4%29
First thing is to know you can break the factors into smaller peices.
sqrt%28252%29+%2A+sqrt%28x%5E3%29+%2A+sqrt%28y%5E4%29
Now factor these smaller pieces with an eye on trying to find factors that are squares. Then do the square root on each of the smaller factors
sqrt%2836%2A7%29+%2A+sqrt%28x%5E2+%2A+x%29+%2A+sqrt%28y%5E4%29
sqrt%2836%29+%2A+sqrt%287%29+%2A+sqrt%28x%5E2%29+%2A+sqrt%28x%29+%2A+sqrt%28y%5E4%29
6+%2A+sqrt%287%29+%2A+x+%2A+sqrt%28x%29+%2A+y%5E2
6xy%5E2%2Asqrt%287x%29