CPM Homework Help : A2C Problem 9-163

For homework, Londa was asked to simplify the expression . She got the answer 7, but when she checked, she learned that the correct answer was −7. Homework Help ✎
1. Show Londa the steps she could take to get −7.
2. What steps do you think Londa took to get 7 as a result?
3. What does she need to consider in order to avoid making this mistake in the future?
4. Londa's example means that it is not always true that for real numbers a and b. What restriction needs to be placed on the numbers a and b?

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

Answer (b):

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

Hint (c):

See parts (a) and (b).

Answer (d):

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