## anonymous 4 years ago How do I simplify: ^3√16 + ^3√54? The answer has to be 5^3√2... how?

1. anonymous

$\sqrt[3]{16} + \sqrt[3]{54}$

2. anonymous

cuberoot(16)+cuberoot(54) =2*cuberoot(2)+3*cuberoot(2) =5*cuberoot(2)

3. anonymous

factor out perfect cubes 16 = 8*2 cube root of 8 is 2

4. anonymous

factor? cube root?

5. anonymous

cuberoot(16)=cuberoot(2)*cuberoot(8) =cuberoot(2)*2

6. anonymous

I'm still kind of confused about ^3√54...

7. anonymous

cuberoot(54)=cuberoot(2)*cuberoot(27) =cuberoot(2)*3

8. anonymous

ohh.. how do I calculate a cuberoot?

9. 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

10. anonymous

ohhh... so how about ^3√54? √2 x 27 = 54, and it's going to be 2*3^3?

11. 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

12. anonymous

=[(2)^(1/3)]*[(3^3)*(1/3)] - I don't do to the power of 1/3 for [(3^3)?

13. anonymous

27=3*3*3=3^3 cuberoot(27)=cuberoot(3^3)=(3^3)^(1/3)=3

14. anonymous

ohhh, okay. thank you!

15. anonymous

np