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

Verified step by step guidance

Start with the given equation: \(27 - x^2 = 0\).

Isolate the squared term by subtracting 27 from both sides: \(-x^2 = -27\).

Multiply both sides by -1 to make the squared term positive: \(x^2 = 27\).

Apply the square root property, which states that if \(x^2 = a\), then \(x = \pm \sqrt{a}\), so write: \(x = \pm \sqrt{27}\).

Simplify the square root if possible by factoring 27 into its prime factors and extracting perfect squares.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

Recommended video:

02:20

Imaginary Roots with the Square Root Property

Related Practice

Textbook Question

Write each number as the product of a real number and i. -√-18

Textbook Question

Solve each inequality. Give the solution set in interval notation. | 3x - 4 | < 2

Textbook Question

Solve each equation. x/(x-1) - 1/(x+1) = 2/(x²-1)

Textbook Question

Solve each equation. 0.5x+ (4/3)x= x+10