1
practice testMultiple Choice

Practice Test

Question 1 • Algebra II

Miguel stated that any monomial can be a cube root. Sylvia disagreed and said that a monomial cube root must have exponents divisible by 3. Who is correct, and why?

Answer
A
Sylvia is correct. Any variable term, when it is cubed, always has an exponent divisible by 3.
B
Miguel is correct. Any monomial can be a perfect cube root because, when it is cubed, the variables will have exponents divisible by 3.
C
Sylvia is correct. In order for the cube to have exponents that are divisible by 3, the cube root has to be divisible by 3.
D
Miguel is correct. Sylvia confused the perfect square root with the perfect cube root.

Explanation

Miguel is correct: any monomial can be used as a cube root, because cubing it multiplies each variable’s exponent by 3. For example, cubing x² gives x⁶, whose exponent is divisible by 3. The cube root’s exponents do not themselves have to be divisible by 3; it is the exponents in the resulting perfect cube that are divisible by 3.

AI-written and checked against the verified answer.

Next