### Home > PC3 > Chapter 5 > Lesson 5.1.3 > Problem5-32

5-32.

​Are the following expressions equivalent? Explain how you know. Try to use at least two different methods to justify your answer.

$(x+2)^{1/2}+(x+2)^{3/2}$ and $(x+3)(x+2)^{1/2}$

Try a few numbers. Do you get the same value for both expressions if:
$x=2$?
$x=7$?
$x=−1$?

Checking a few numbers does not prove that the expressions are equivalent.
Can you algebraically rewrite one expression so that it is the same as the other expression?