Question

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

Answer 1

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

Answer 2

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

Answer 3

factor out perfect cubes

16 = 8*2
cube root of 8 is 2

Answer 4

factor? cube root?

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

ohh.. how do I calculate a cuberoot?

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

ohhh, okay. thank you!

Answer 15

np