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:

$(-6)^2 = 6^2$

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