How do you solve #sqrt(x^2)=6#?

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Answer 1 · 2017-01-08T00:31:59

#color(blue)(x)=color(blue)6#

#sqrt(x^2)=6#

#sqrt(x^2)=x#

#color(blue)(x)=color(blue)6#

Check.

#sqrt(6^2)=6#

#6=6#

Answer 2 · 2017-01-08T00:48:57

#x = +-6#

The difference of squares identity can be written:

#a^2-b^2 = (a-b)(a+b)#

We use this below with #a=x# and #b=6#.

Given:

#sqrt(x^2) = 6#

Note that both #sqrt(...) >= 0# and #6 >= 0#. So we can safely square both sides of the equation, without introducing extraneous solutions and find:

#x^2 = 6^2#

Subtract #6^2# from both sides to get:

#0 = x^2-6^2 = (x-6)(x+6)#

So #x = +-6#

Both of these values satisfy the original equation since:

#(-6)^2 = 6^2#