Solve for x square root of x^2 = square root of 144

$\sqrt{x^{2}} = \sqrt{144}$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x^{2}}}^{2} = {\sqrt{144}}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{2}}$ as $x^{\frac{2}{2}}$ .

${(x^{\frac{2}{2}})}^{2} = {\sqrt{144}}^{2}$

Divide $2$ by $2$ .

${(x^{1})}^{2} = {\sqrt{144}}^{2}$

Simplify the left side.

Multiply the exponents in ${(x^{1})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{1 \cdot 2} = {\sqrt{144}}^{2}$

Multiply $2$ by $1$ .

$x^{2} = {\sqrt{144}}^{2}$

Simplify the right side.

Simplify ${\sqrt{144}}^{2}$ .

Rewrite $144$ as $12^{2}$ .

$x^{2} = {\sqrt{12^{2}}}^{2}$

Pull terms out from under the radical, assuming positive real numbers.

$x^{2} = 12^{2}$

Raise $12$ to the power of $2$ .

$x^{2} = 144$

Step 3

Solve for $x$ .

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{144}$

Simplify $\pm \sqrt{144}$ .

Rewrite $144$ as $12^{2}$ .

$x = \pm \sqrt{12^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 12$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 12$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 12$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 12, - 12$