limit as h approaches 0

Question

cubed root of 8+h -2
divided by h

the cubed root sign is under 8+h and not -2

A. 1/12
B.1/4
C.root 2 over 2
D.root 2
E.2

Answer is A but can someone explain

Answer 1

Recall that (a^3-b^3) = (a-b)(a^2+ab+b^2)
Now let a^3 = 8+h and b^3 = 8 and you have
(8+h)-8 = (∛(8+h)-∛8)(∛(8+h)^2 + ∛((8+h)(8)) + ∛8^2)
= (∛(8+h)-2)(∛(8+h)^2+2∛(8+h)+4)

Thus,
(∛(8+h)-2)/h =

(∛(8+h)-2)(∛(8+h)^2+2∛(8+h)+4)
------------------------------------------------
h(∛(8+h)^2+2∛(8+h)+4)

(8+h)-8
------------------------------------------------
h(∛(8+h)^2+2∛(8+h)+4)

= h/(h(∛(8+h)^2+2∛(8+h)+4))
= 1/(∛(8+h)^2+2∛(8+h)+4)
Now let h->0 and you get
1/(∛(8)^2+2∛(8)+4) =1/(4+4+4) = 1/12

Answer 2

We didnt learn that way is there another way to do it