Simplify the radical expression. (Multiple Choice)

Question

 

a. 2g²

b. 2g³

c. 2|g³|

d. 2|g^2|

Answer 1

In a normal square root, you can factor everything inside the radical and then "take out" factors that occur twice:

 

√(12y²) = √(2×2×3×y×y) = 2y√(3)

 

That's because an expression with two of the same factors like √(2×2) = √(2²) = 2.

 

 

 

A similar process takes place with cube roots, but this time, we can "take out" factors that occur three times. So:

 

^₃√(8g⁶) = ^₃√(2×2×2×g×g×g×g×g×g)

 

There are three 2's and two groups of three g's. So, we'll take out a 2 and two g's. That leaves us with:

 

2g²