Find all the real cube roots of 216. (Multiple Choice)

Question

a. -6
b. 6
c. -6 and 6
d. no real roots

Answer 1

A cube root of 216 is a solution of the equation x³ = 216

 

If x³ = 216, then x³ - 216 = 0

 

                              x³ - 6³ = 0 

 

A³ - B³ = (A - B)(A² + AB + B²)

 

x³ - 6³ = (x - 6)(x² + 6x + 36) = 0

 

If x- 6 = 0, then x = 6.

If x² + 6x + 36 = 0, then by the quadratic formula, we can show that x is imaginary.

 

Therefore, the only real cube root of 216 is 6.  

Answer 2

The answer is 6

 

if you raise a negative number to an odd power the answer is negative.

 

6³ = 6(6)(6)=36(6)=216

 

(-6)³ = (-6)(-6)(-6) = 36(-6) = -216