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

##### 2 Answers

Apr 15, 2018

Refer to the explanation.

#### Explanation:

**law of indices : #root(n)(a^m) rArr a^(m/n)#**

Hope this helps :)

Apr 15, 2018

See below.

#### Explanation:

To be more accurate,

Let's consider two cases:

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