SOLUTION: Given an example to show that the sqrt{a^2} is not equal to a.
Use it to explain why sqrt{a^2} = | a |.
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Question 1208654: Given an example to show that the sqrt{a^2} is not equal to a.
Use it to explain why sqrt{a^2} = | a |.
Answer by Shin123(626) (Show Source): You can put this solution on YOUR website!
For an example, let's say . Then, , which is not equal to -1.
Note that the square root function always takes the principal square root (the nonnegative one). If is positive, then will still be , since that is the principal square root. If is negative, then will be , since the two square roots are and , and is the principal square root. ( is negative, so is positive). If is 0, then is also just . Note that this is the exact definition of |a|. The absolute value function leaves positive numbers and zero unchanged, while taking the negative of negative numbers to make them positive. (same thing the square root function did).
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