SOLUTION: Give an example to show that sqrt{a^(2)} is not equal to a. Use it to explain why sqrt{a^(2)} = | a |. 

Algebra ->  Square-cubic-other-roots -> SOLUTION: Give an example to show that sqrt{a^(2)} is not equal to a. Use it to explain why sqrt{a^(2)} = | a |.        Log On


   

Question 1198887: Give an example to show that sqrt{a^(2)} is not equal to a. Use it to explain why sqrt{a^(2)} = | a |. 

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Consider a+=+-5

Let's plug that into the equation below and simplify both sides.
sqrt%28a%5E2%29+=+a

sqrt%28%28-5%29%5E2%29+=+-5

sqrt%2825%29+=+-5

5+=+-5
We get a contradiction which shows the formula doesn't work for a+=+-5
Similar contradictions happen whenever 'a' is negative.

If we were to require that a+%3E=0+ (i.e. 'a' is nonnegative), then sqrt%28a%5E2%29+=+a would be true.

However, for all real numbers, we must use absolute value to ensure the result is positive.
So that's why we go for sqrt%28a%5E2%29+=+abs%28a%29