Question

How do you solve `a^3 = 216`?

Answer 1

See the solution process below:

Explanation:

`a^3 = 216` can be rewritten as:

`a * a * a = 6 * 6 * 6`

Therefore:

`a = 6`

Answer 2

`6`.

Explanation:

There are 2 possible methods, the first one has a simpler approach:

1) To solve this problem, realize that the number `216` can be factored and rewritten as

`216 = 6^3 = 6*6*6`

Therefore, you can rewrite the equation as

`a^3=6^3`

Since both sides contain a cube, `""^3`, you can use the property of equality to say that `a=6`.

2) This solution will be more likely what you are looking for if you are in Algebra 2 or around that level in mathematics. First, you would subtract `216` from both sides to get

`a^3 - 216=0`

Then, you use the "difference of cubes" factorization method to rewrite this as

`(a-6)(a^2 + 6a + 36) = 0`

Then, you would find the "zeros" of the equation, and there is only one real solution: `6`.