# How do you solve a^3 = 216?

Apr 23, 2017

See the solution process below:

#### Explanation:

${a}^{3} = 216$ can be rewritten as:

$a \cdot a \cdot a = 6 \cdot 6 \cdot 6$

Therefore:

$a = 6$

Apr 23, 2017

$6$.

#### 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

$216 = {6}^{3} = 6 \cdot 6 \cdot 6$

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

$\left(a - 6\right) \left({a}^{2} + 6 a + 36\right) = 0$

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