SOLUTION: I am really struggling with these... Please help. Multiply: (9-√5)(3+√5) Multiply and simplify by factoring. ³√y^7 ³√16y^8

Algebra ->  Radicals -> SOLUTION: I am really struggling with these... Please help. Multiply: (9-√5)(3+√5) Multiply and simplify by factoring. ³√y^7 ³√16y^8      Log On


   

Question 564678: I am really struggling with these... Please help.
Multiply:
(9-√5)(3+√5)
Multiply and simplify by factoring.
³√y^7 ³√16y^8
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply:
(9-√5)(3+√5)
----
Use FOIL:
F: 27
O:9*sqrt(5)
I:-3*sqrt(5)
L: -5
----
= 22 + 6sqrt(5)
==================================
Multiply and simplify by factoring.
³√y^7 ³√16y^8
----
= [16y^15]^(1/3)
----
= [8y^15*2]^(1/3)
-----
= 2y^5*cbrt(2)
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Cheers,
Stan H.
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Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
%289-sqrt%285%29%29%283%2Bsqrt%285%29%29

9(3+sqrt(5)-sqrt(5)(3+sqt(5))

27+9sqrt(5)-3sqrt(5)-5
22+6sqrt(5)
-------------
cuberoot(y^7)*cuberoot(16y^8)
y^2*cuberoot(y)*2y^2cuberoot(2y^2)
y*2*2y^2*cuberoot(y*2y^2)
2y^4*cuberoot(2y^3)
2y^4*y(cuberoot(2))
2y^5*cuberoot(2)