SOLUTION: 5y sqrt(8y)+2 sqrt(50y^3)

Algebra ->  Radicals -> SOLUTION: 5y sqrt(8y)+2 sqrt(50y^3)      Log On


   

Question 612956: 5y sqrt(8y)+2 sqrt(50y^3)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
5y%2Asqrt%288y%29%2B2%2Asqrt%2850y%5E3%29
The two terms, as they stand, are not like terms so we cannot add them together. But both square roots have perfect square factors so we can simplify each one:
5y%2Asqrt%284%2A2y%29%2B2%2Asqrt%2825%2Ay%5E2%2A2y%29
5y%2Asqrt%284%29%2Asqrt%282y%29%2B2%2Asqrt%2825%29%2Asqrt%28y%5E2%29%2Asqrt%282y%29
5y%2A2%2Asqrt%282y%29%2B2%2A5%2Ay%2Asqrt%282y%29
Note: Because the initial square roots had odd powers of y, we know that y cannot be negative. So an absolute value is not necessary around the "y" we got from sqrt%28y%5E2%29.
Continuing to simplify...
10y%2Asqrt%282y%29%2B10y%2Asqrt%282y%29

Now that the square roots are simplified, we happen to have like terms that can be added together! (Note: This does not always happen.) Adding the terms together we get:
20y%2Asqrt%282y%29