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

2 Answers
Apr 15, 2018

Answer:

#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 :)

Apr 15, 2018

Answer:

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#.