This page is part of my unofficial solutions manual to the GRE Paper Practice Book (2e), a free resource available on the ETS website. They publish the questions; I explain the answers. If you haven’t worked through the Practice Book, give Section 6 a shot before reading this!

6.21: Cube Root, Square Root

With the chart block out of the way, we’re in the home stretch. This problem basically tests your knowledge of the relationship between roots (square, cube, etc.) and exponents. Specifically, they’re checking to see if you know how to “undo” the square root and cube root operations:

Here, we apply the rules as follows:

• Since 3 is the cube root of x, 3 cubed gives us the value of x.
  
  
• Since x is the square root of y, x squared gives us the value of y.
  
  

Math Review Reference

For more on this topic, see the following section of the GRE Math Review:

• 1.3: Exponents and Roots (p. 5)