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

Jan 8, 2017

$\textcolor{b l u e}{x} = \textcolor{b l u e}{6}$

#### Explanation:

$\sqrt{{x}^{2}} = 6$

$\sqrt{{x}^{2}} = x$

$\textcolor{b l u e}{x} = \textcolor{b l u e}{6}$

Check.

$\sqrt{{6}^{2}} = 6$

$6 = 6$

Jan 8, 2017

$x = \pm 6$

#### Explanation:

The difference of squares identity can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

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

Given:

$\sqrt{{x}^{2}} = 6$

Note that both $\sqrt{\ldots} \ge 0$ and $6 \ge 0$. 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:

$0 = {x}^{2} - {6}^{2} = \left(x - 6\right) \left(x + 6\right)$

So $x = \pm 6$

Both of these values satisfy the original equation since:

${\left(- 6\right)}^{2} = {6}^{2}$