SOLUTION: Please walk me through each step in solving this problem: Simplify by collecting like radical terms, if possible: 3times the cube root of y^5 + 4 times cube root of y

Algebra ->  Radicals -> SOLUTION: Please walk me through each step in solving this problem: Simplify by collecting like radical terms, if possible: 3times the cube root of y^5 + 4 times cube root of y      Log On


   

Question 200828: Please walk me through each step in solving this problem:
Simplify by collecting like radical terms, if possible:
3times the cube root of y^5 + 4 times cube root of y^2 + cube root of 8y^6.
They say the answer is (3y+4)times cube root of y^2 + 2y^2.
Sorry I cannor provide the symbol for square root.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Aroot%283%2Cy%5E5%29%2B4%2Aroot%283%2Cy%5E2%29%2Broot%283%2C8y%5E6%29 Start with the given expression.


3%2Aroot%283%2Cy%5E5%29%2B4%2Aroot%283%2Cy%5E2%29%2Broot%283%2C2%5E3%2Ay%5E6%29 Rewrite 8 as 2%5E3


3%2Aroot%283%2Cy%5E3%2Ay%5E2%29%2B4%2Aroot%283%2Cy%5E2%29%2Broot%283%2C2%5E3%2Ay%5E6%29 Rewrite y%5E5 as y%5E3%2Ay%5E2


Rewrite y%5E6 as y%5E3%2Ay%5E3


Break up the roots using the identity root%28n%2Cx%2Ay%29=root%28n%2Cx%29%2Aroot%28n%2Cy%29


Evaluate the cube root of 2%5E3 to get 2


3%2Ay%2Aroot%283%2Cy%5E2%29%2B4%2Aroot%283%2Cy%5E2%29%2B2%2Ay%2Ay Evaluate the cube root of y%5E3 to get "y"


3%2Ay%2Aroot%283%2Cy%5E2%29%2B4%2Aroot%283%2Cy%5E2%29%2B2y%5E2 Multiply


%283y%2B4%29%2Aroot%283%2Cy%5E2%29%2B2y%5E2 Factor out the root%283%2Cy%5E2%29 from the first two terms. note: this step isn't necessary, but your book does it.


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Answer:


So 3%2Aroot%283%2Cy%5E5%29%2B4%2Aroot%283%2Cy%5E2%29%2Broot%283%2C8y%5E6%29 simplifies to %283y%2B4%29%2Aroot%283%2Cy%5E2%29%2B2y%5E2



In other words,