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anonymous

  • 4 years ago

How do I simplify: ^3√16 + ^3√54? The answer has to be 5^3√2... how?

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  1. anonymous
    • 4 years ago
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    \[\sqrt[3]{16} + \sqrt[3]{54}\]

  2. anonymous
    • 4 years ago
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    cuberoot(16)+cuberoot(54) =2*cuberoot(2)+3*cuberoot(2) =5*cuberoot(2)

  3. dumbcow
    • 4 years ago
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    factor out perfect cubes 16 = 8*2 cube root of 8 is 2

  4. anonymous
    • 4 years ago
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    factor? cube root?

  5. anonymous
    • 4 years ago
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    cuberoot(16)=cuberoot(2)*cuberoot(8) =cuberoot(2)*2

  6. anonymous
    • 4 years ago
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    I'm still kind of confused about ^3√54...

  7. anonymous
    • 4 years ago
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    cuberoot(54)=cuberoot(2)*cuberoot(27) =cuberoot(2)*3

  8. anonymous
    • 4 years ago
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    ohh.. how do I calculate a cuberoot?

  9. anonymous
    • 4 years ago
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    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

  10. anonymous
    • 4 years ago
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    ohhh... so how about ^3√54? √2 x 27 = 54, and it's going to be 2*3^3?

  11. anonymous
    • 4 years ago
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    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

  12. anonymous
    • 4 years ago
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    =[(2)^(1/3)]*[(3^3)*(1/3)] - I don't do to the power of 1/3 for [(3^3)?

  13. anonymous
    • 4 years ago
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    27=3*3*3=3^3 cuberoot(27)=cuberoot(3^3)=(3^3)^(1/3)=3

  14. anonymous
    • 4 years ago
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    ohhh, okay. thank you!

  15. anonymous
    • 4 years ago
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    np

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