1Cademy - Solving $$x^2 = 9$$ Using the Square Root Property

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Quadratic Equation

Example

Solving $x^2 = 9$ Using the Square Root Property

Solve $x^2 = 9$ by applying the Square Root Property instead of factoring.

Apply the Square Root Property directly: $x = \pm\sqrt{9}$ .

Simplify the radical, since $9$ is a perfect square: $x = \pm 3$ .

Rewrite to show the two individual solutions: $x = 3$ or $x = -3$ .

This yields the same result as solving by factoring — rewriting as $x^2 - 9 = 0$ , factoring the left side as $(x - 3)(x + 3) = 0$ , and applying the Zero Product Property — but the Square Root Property reaches the answer more directly, bypassing the need to put the equation in standard form, factor, and set each factor equal to zero.