### Home > CCA2 > Chapter 8 > Lesson 8.3.2 > Problem8-163

8-163.

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 $-7$.

$\sqrt{-7} \cdot \sqrt{-7} = i\sqrt{7} \cdot i\sqrt{7}$

$=i^2\sqrt{49}$

$-1\sqrt{49}$

$= -1 \cdot 7 = -7$

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

Look at the negative signs.

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

Convert to imaginary form before completing operations.

3. 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 $b$?

They must be non-negative real numbers.