1Cademy - Solving $$x^2 = 7$$ Using the Square Root Property

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Quadratic Equation

Example

Solving $x^2 = 7$ Using the Square Root Property

Solve $x^2 = 7$ by applying the Square Root Property. Since $7$ is not a perfect square, this equation cannot be solved by factoring — there is no way to express $x^2 - 7$ as a product of binomials with integer coefficients.

Apply the Square Root Property: $x = \pm\sqrt{7}$ .

Rewrite as two separate solutions: $x = \sqrt{7}$ or $x = -\sqrt{7}$ .

Because $7$ is prime and has no perfect square factors, $\sqrt{7}$ cannot be simplified further, so the solutions are left in radical form. This example illustrates the key advantage of the Square Root Property over factoring: it works regardless of whether the constant is a perfect square.