SOLUTION: I知 really confusing with this factoring, Can anyone please help me with step by step? Thank you very much! Simplify by factoring. 1.4*sqrt(405x^8y^10)=? 2.5*sqrt(64x^12y^15

Algebra ->  Radicals -> SOLUTION: I知 really confusing with this factoring, Can anyone please help me with step by step? Thank you very much! Simplify by factoring. 1.4*sqrt(405x^8y^10)=? 2.5*sqrt(64x^12y^15      Log On


   

Question 212370: I知 really confusing with this factoring, Can anyone please help me with step by step? Thank you very much!
Simplify by factoring.
1.4*sqrt(405x^8y^10)=?
2.5*sqrt(64x^12y^15)=?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you going in the right direction.

# 1


4%2Asqrt%28405x%5E8y%5E10%29 Start with the given expression.


4%2Asqrt%28405%29%2Asqrt%28x%5E8%29%2Asqrt%28y%5E10%29 Break up the square root using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29


4%2Asqrt%2881%2A5%29%2Asqrt%28x%5E8%29%2Asqrt%28y%5E10%29 Factor 405 into 81*5


4%2Asqrt%289%5E2%2A5%29%2Asqrt%28x%5E8%29%2Asqrt%28y%5E10%29 Rewrite 81 as 9%5E2


4%2Asqrt%289%5E2%2A5%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28y%5E10%29 Rewrite x%5E8 as %28x%5E4%29%5E2


4%2Asqrt%289%5E2%2A5%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28%28y%5E5%29%5E2%29 Rewrite y%5E10 as %28y%5E5%29%5E2


4%2Asqrt%289%5E2%29%2Asqrt%285%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28%28y%5E5%29%5E2%29 Break up the first square root (using that same identity)


4%2A9%2Asqrt%285%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28%28y%5E5%29%5E2%29 Take the square root of 9%5E2 to get 9 (notice how the squares and the square roots 'undo' each other).


4%2A9%2Asqrt%285%29%2Ax%5E4%2Asqrt%28%28y%5E5%29%5E2%29 Take the square root of %28x%5E4%29%5E2 to get x%5E4.


4%2A9%2Asqrt%285%29%2Ax%5E4%2Ay%5E5 Take the square root of %28y%5E5%29%5E2 to get y%5E5.


36x%5E4y%5E5%2Asqrt%285%29 Rearrange the terms.


So 4%2Asqrt%28405x%5E8y%5E10%29=36x%5E4y%5E5%2Asqrt%285%29 where every variable is nonnegative.