Imaginary Numbers Equation

[codys4]

My friend asked me for help on this equation. We both got the answers 36 and the study guide said the answer was 53. Well i finally got the answer 53 but while i was solving i remembered that negative numbers under a square root mean that they become imaginary. So what makes the answer 53 and not 68 - 15i. (see attached pictures)

(see attached picture for equation)

Which answer is correct?

 

[skeeter]

note that [MATH]\sqrt{x^2} = |x|[/MATH] ...

[MATH]-(-5)^0 - 3[-5 - 2(3)^2+ |-5|][/MATH]
[MATH]-1 - 3[-5 - 18 + 5][/MATH]
[MATH]-1 - 3(-18)[/MATH]
[MATH]-1 + 54[/MATH]
[MATH]53[/MATH]

 

[Dr.Peterson]

You entered the radical once as \(\sqrt{(-5)^2}\), and once as \(\sqrt{-5^2}\). Only the former represents what you were given, which is \(\sqrt{x^2}\) where \(x = -5\).

You have to use parentheses when plugging in the value so that it means what you intend, which is that you square x, which is -5.

Without the parentheses, the -5 is ripped apart into a negative and a 5, with only the latter being squared. Such violence can't be condoned.

 

[Steven G]

So you think that (-5)^2 is negative?

 

[HallsofIvy]

There are NO imaginary numbers in this problem. \(\displaystyle (-5)^2= 25\) which is positive. Note the parentheses.