Can someone help me simplify this 1 radical? Thanks!

Question

anonymous · Answer

https://gcs490.brainhoney.com/Resource/14610120,45A,0,0/Assets/flvs/algebra2_v10_gs-xml/res0046/04_02c_10_1.gif

jim_thompson5910 · Answer

Are you familiar with perfect cube numbers?

anonymous · Answer

not really

anonymous · Answer

If you could provide an answer, with how you got it, so I can study that, it would be helpful!

jim_thompson5910 · Answer

you're familiar with perfect squares right?

1, 4, 9, 16, 25, ...

numbers like that

jim_thompson5910 · Answer

Well anyway, the list of perfect cubes are

1, 8, 27, 64, 125, ...

since

1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
....
....

jim_thompson5910 · Answer

you then use this list to help you simplify each radical

since 54 = 27*2, we can say this


$$\large \sqrt[3]{54} = \sqrt[3]{27*2}$$


$$\large \sqrt[3]{54} = \sqrt[3]{27}*\sqrt[3]{2}$$


$$\large \sqrt[3]{54} = \sqrt[3]{3^3}*\sqrt[3]{2}$$


$$\large \sqrt[3]{54} = 3*\sqrt[3]{2}$$

jim_thompson5910 · Answer

You apply the same basic steps to the other radicals. Once they are simplified fully, you combine like terms