Evaluate square root of x^2=3

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Algebra

$\sqrt{x^{2}} = 3$

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

${\sqrt{x^{2}}}^{2} = 3^{2}$

Simplify each side of the equation.

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

${(x^{\frac{2}{2}})}^{2} = 3^{2}$

Divide $2$ by $2$ .

${(x^{1})}^{2} = 3^{2}$

Simplify the left side.

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

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

$x^{1 \cdot 2} = 3^{2}$

Multiply $2$ by $1$ .

$x^{2} = 3^{2}$

Simplify the right side.

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Raise $3$ to the power of $2$ .

$x^{2} = 9$

Solve for $x$ .

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

$x = \pm \sqrt{9}$

Simplify $\pm \sqrt{9}$ .

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Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

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

$x = \pm 3$

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

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

$x = 3$

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

$x = - 3$

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

$x = 3, - 3$

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