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

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

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) (Show Source): You can put this solution on YOUR website!

Consider

Let's plug that into the equation below and simplify both sides.

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

If we were to require that (i.e. 'a' is nonnegative), then 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

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