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 $−7$.

   Step 1(a):

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

   Step 2(a):

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

   Answer (a):

   $−7$

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

   Answer (b):

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

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

   Hint (c):

   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?

   Answer (d):

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