Solve each equation in Exercises 15–34 by the square root property. $3x^2=27$

Verified step by step guidance

1. Start with the given equation: \$3x^2 = 27$.
2. Isolate the \(x^2\) term by dividing both sides of the equation by 3: \(x^2 = \frac{27}{3}\).
3. Simplify the right side to get \(x^2 = 9\).
4. Apply the square root property, which states that if \(x^2 = a\), then \(x = \pm \sqrt{a}\), so here \(x = \pm \sqrt{9}\).
5. Simplify the square root to express the solutions for \(x\).

Key Concepts

Square Root Property

The square root property states that if x² = k, then x = ±√k. This property is used to solve quadratic equations that can be written in the form x² = a constant, allowing you to find the values of x by taking the square root of both sides.

Isolating the Variable Term

Before applying the square root property, the equation must be manipulated so that the squared term is isolated on one side. This often involves dividing or multiplying both sides of the equation to simplify it to the form x² = number.

Simplifying Square Roots

After taking the square root of both sides, it is important to simplify the radical expression. This includes factoring out perfect squares and expressing the root in simplest form, which helps in finding exact solutions.