Solve each equation using the square root property. 27 - x² = 0

Verified step by step guidance

1. Start with the given equation: \$27 - x^2 = 0$.
2. Isolate the squared term by subtracting 27 from both sides: \(-x^2 = -27\).
3. Multiply both sides by -1 to make the squared term positive: \(x^2 = 27\).
4. Apply the square root property, which states that if \(x^2 = a\), then \(x = \pm \sqrt{a}\), so write: \(x = \pm \sqrt{27}\).
5. Simplify the square root if possible by factoring 27 into its prime factors and extracting perfect squares.

Key Concepts

Square Root Property

The square root property states that if x² = k, then x = ±√k. This method is used to solve equations where the variable is squared and isolated on one side. It allows for finding both positive and negative roots of the equation.

Isolating the Variable Term

Before applying the square root property, the equation must be rearranged so that the squared term stands alone on one side. This involves moving constants or other terms to the opposite side through addition or subtraction.

Simplifying Square Roots

After isolating the squared term and applying the square root property, simplifying the square root expression is necessary. This includes reducing radicals to simplest form and expressing answers in exact or decimal form as required.