1Cademy - Solving $$x^2 = 169$$ Using the Square Root Property

Learn Before

Square Root Property

Example

Solving $x^2 = 169$ Using the Square Root Property

Solve $x^2 = 169$ by applying the Square Root Property, since $169$ is a perfect square.

Apply the Square Root Property: $x = \pm\sqrt{169}$ .

Simplify the radical. Because $13^2 = 169$ , the principal square root of $169$ is $13$ : $x = \pm 13$ .

Rewrite to show the two individual solutions: $x = 13$ or $x = -13$ .

Since $169$ is a perfect square, the radical simplifies to an integer, producing two integer solutions. This follows the same pattern as solving $x^2 = 9$ : the Square Root Property immediately yields $\pm\sqrt{k}$ , and because $k$ is a perfect square, the answer is a pair of integers rather than expressions in radical form.