Solve for a square root of a^2=17

$\sqrt{a^{2}} = 17$

Step 1

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

${\sqrt{a^{2}}}^{2} = 17^{2}$

Step 2

Simplify each side of the equation.

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

${(a^{\frac{2}{2}})}^{2} = 17^{2}$

Divide $2$ by $2$ .

${(a^{1})}^{2} = 17^{2}$

Simplify the left side.

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

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

$a^{1 \cdot 2} = 17^{2}$

Multiply $2$ by $1$ .

$a^{2} = 17^{2}$

Simplify the right side.

Raise $17$ to the power of $2$ .

$a^{2} = 289$

Step 3

Solve for $a$ .

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

$a = \pm \sqrt{289}$

Simplify $\pm \sqrt{289}$ .

Rewrite $289$ as $17^{2}$ .

$a = \pm \sqrt{17^{2}}$

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

$a = \pm 17$

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.

$a = 17$

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

$a = - 17$

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

$a = 17, - 17$