### Home > INT3 > Chapter 5 > Lesson 5.1.2 > Problem5-38

5-38.
1. For homework, Crystal must simplify the expression . She gets the answer 3, but when she checks, she learns that the correct answer is –3. Homework Help ✎

1. Show Crystal the steps she could take to get –3.

2. What steps do you think Crystal took to get 3 as a result?

3. What does she need to consider to avoid making this mistake in the future?

4. Crystal’s example means that is not always true for real numbers a and b. What restriction needs to be placed on the numbers a and b?

$\sqrt{-3} \cdot \sqrt{-3} = i\sqrt{3} \cdot i\sqrt{3}$

$i^2\sqrt{9}$

$-1\sqrt{9}$

$-1 \cdot 3 = -3$

What is (−3)(−3)?

She needs to convert to imaginary form before completing operations.

They must be non-negative real numbers.