anonymous
  • anonymous
How do I simplify: ^3√16 + ^3√54? The answer has to be 5^3√2... how?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\sqrt[3]{16} + \sqrt[3]{54}\]
anonymous
  • anonymous
cuberoot(16)+cuberoot(54) =2*cuberoot(2)+3*cuberoot(2) =5*cuberoot(2)
dumbcow
  • dumbcow
factor out perfect cubes 16 = 8*2 cube root of 8 is 2

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anonymous
  • anonymous
factor? cube root?
anonymous
  • anonymous
cuberoot(16)=cuberoot(2)*cuberoot(8) =cuberoot(2)*2
anonymous
  • anonymous
I'm still kind of confused about ^3√54...
anonymous
  • anonymous
cuberoot(54)=cuberoot(2)*cuberoot(27) =cuberoot(2)*3
anonymous
  • anonymous
ohh.. how do I calculate a cuberoot?
anonymous
  • anonymous
there are ways to approximate it, but lets say you are trying to find cuberoot(y) just find a number x which satisfies x*x*x=y
anonymous
  • anonymous
ohhh... so how about ^3√54? √2 x 27 = 54, and it's going to be 2*3^3?
anonymous
  • anonymous
cuberoot is a number to the exponent 1/3 so ^3√54 =(54)^(1/3) =(2*27)^(1/3) =(2*3^3)^(1/3) =[(2)^(1/3)]*[(3^3)*(1/3)] =[(2)^(1/3)]*3 =3* ^3√2
anonymous
  • anonymous
=[(2)^(1/3)]*[(3^3)*(1/3)] - I don't do to the power of 1/3 for [(3^3)?
anonymous
  • anonymous
27=3*3*3=3^3 cuberoot(27)=cuberoot(3^3)=(3^3)^(1/3)=3
anonymous
  • anonymous
ohhh, okay. thank you!
anonymous
  • anonymous
np

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