Why does this equal 2? \sqrt[3]{8}

Question

Why does this equal 2?


`\sqrt[3]{8}`

Answer 1

If you use the prime factorization method to solve for 8, you will find that you get three multiples of 8, which are 2,2 and 2. Since the root is a (power 3), you have to group three same numbers together into one and it wil be out of root.

Answer 2

The prime factorization of 8 is 2³
and ∛8 =
`8^{ (1)/(3) }`

So if you make the replacements


`(2 ^(3))^ (1)/(3)` using exponent laws you would multiply the powers resulting in
`2^(1)` = 2 because 3 × 1/3 = 1