### Home > A2C > Chapter 9 > Lesson 9.3.2 > Problem9-163

9-163.

For homework, Londa was asked to simplify the expression $\sqrt { - 7 } \cdot \sqrt { - 7 } =$. She got the answer $7$, but when she checked, she learned that the correct answer was $−7$.

1. Show Londa the steps she could take to get $−7$.

First eliminate the negative sign from each radical by replacing it with $i$.

Remember that $i$ is the square root of $−1$, now finish multiplying.

$−7$

2. What steps do you think Londa took to get $7$ as a result?

$\text{Londa multiplied }\sqrt{-7}\cdot\sqrt{-7}\text{ to get }\sqrt{49} = 7$

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

See parts (a) and (b).

4. Londa's example means that it is not always true that$\sqrt { a } \cdot \sqrt { b } = \sqrt { a b }$ for real numbers a and b. What restriction needs to be placed on the numbers a and b?

The variables a and b must be non-negative real numbers.