Question

How do you simplify `sqrt(a^2)`?

Answer 1

`a`
Refer to the explanation.

Explanation:

`sqrt(a^2) rArr a^(2/2) rArr a`
law of indices : `root(n)(a^m) rArr a^(m/n)`

Hope this helps :)

Answer 2

See below.

Explanation:

To be more accurate, `sqrt(a^2) = abs a`...

Let's consider two cases: `a>0` and `a<0`.

Case 1: `a>0`

Let `a = 3`. Then `sqrt (a^2) = sqrt(3^2) = sqrt 9 = 3 = a`.
In this case, `sqrt (a^2) = a`.

Case 2: `a<0`

Let `a = -3`. Then `sqrt (a^2) = sqrt ((-3)^2) = sqrt 9 = 3 != a`. In this case, `sqrt (a^2) != a`. However, it does equal `abs a` because `abs (-3) = 3`.

Whether `a>0` or `a<0`, `sqrt (a^2) > 0`; it will always be positive. We account for this with the absolute value sign: `sqrt (a^2) = abs a`.