Fourth Edition Strategy guide EIV pg. 79 #2

[afvatcha]

I don't understand why there are two answers.

^2+6+9 is (x+3)(x+3). So in both circumstances the answer would be -3.

Which brings me to my next Question. I thought you couldnt have negs. inside a square root.

[jnelson0612]

I don't understand why there are two answers.

^2+6+9 is (x+3)(x+3). So in both circumstances the answer would be -3.

Which brings me to my next Question. I thought you couldnt have negs. inside a square root.

This one is tricky. I can understand your confusion, and you are right that we can never have a negative under the square root sign. However, that's not what we have here.

This problem hinges on the fact that we don't know what d is. d could be positive or negative. What if d is negative? Well, even if it is negative, when we take (d+3) and square it, it will become positive, so we can then take the square root. For example, if d=-5, then -5 + 3 = -2, but squared that is 4. We can take the square root of 4, which is 2. Thus, you can see that we are not actually ever going to be taking the square root of a negative number.

So, if d is a positive number, it is (d+3) that is the square root of that expression.
If d is a negative number, it's actually -(d+3) that results as the square root of the expression. Using d=-5, -(-5+3) = 2, which is our square root.

I hope this makes more sense!