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

Answer 1

Ethan Adkins

#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#

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Answer 2

Genesis Allen

#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#

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Answer 3

Julia Adams

To solve the equation sqrt(x^2) = 6, we need to isolate x. Taking the square root of both sides, we get |x| = 6. Since the square root of a number is always positive, we can remove the absolute value and obtain x = 6 or x = -6 as the solutions.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.