ASVAB Mathematics Knowledge Practice: Cube and Square Roots

Some questions on the Mathematics Knowledge subtest on the ASVAB are guaranteed to be totally radical. Not in the '80s sense, but because they deal with numbers that are square and cube roots of other numbers.

Practice questions

1. Solve

   

   when x = –3.

   A. 15² B. 25 C. 1.5 D. 15

2. Given

   

   simplify the expression.

   

Answers and explanations

1. The correct answer is Choice (D).

   First evaluate the expression inside the square root symbol by filling in the value of x:

   

   Find

   

   by determining that

   

2. The correct answer is Choice (C).

   Both radicals are cube roots, so multiply the radicands. Because

   

   you get

   

   Factor and simplify, and look for perfect cubes to make it easier:

   

   Rewrite the numbers and variables as the product of radicals so you continue to work with like terms:

   

   Solve what you can and simplify: