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

2 Answers
Apr 23, 2017

Answer:

See the solution process below:

Explanation:

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

#a * a * a = 6 * 6 * 6#

Therefore:

#a = 6#

Answer:

#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#.