Textbook Question
Write each number as the product of a real number and i. -√-18
Ch. 1 - Equations and Inequalities
Lial13th EditionCollege AlgebraISBN: 9780136881063
Not the one you use?Change textbookSelect a different textbook
Table of contents
Chapter 2, Problem 28
Solve each equation using the square root property. 48 - x2 = 0
Verified step by step guidance1
Start with the given equation: \(48 - x^2 = 0\).
Isolate the squared term by subtracting 48 from both sides: \(-x^2 = -48\).
Multiply both sides by \(-1\) to make the squared term positive: \(x^2 = 48\).
Apply the square root property, which states that if \(x^2 = a\), then \(x = \pm \sqrt{a}\): \(x = \pm \sqrt{48}\).
Simplify the square root if possible by factoring 48 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:
1mWas 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. Applying this property allows you to find both positive and negative roots of the equation.
Recommended video:
02:20
Imaginary Roots with the Square Root Property
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 the equation for easier solving.
Recommended video:
Guided course
05:28Equations with Two Variables
Simplifying Square Roots
After isolating the squared term and taking the square root, simplify the radical if possible. This includes factoring out perfect squares to write the root in simplest form, which helps in expressing the exact solutions clearly.
Recommended video:
02:20Imaginary Roots with the Square Root Property
Related Practice
Textbook Question
Solve each inequality. Give the solution set in interval notation. | 3x - 4 | < 2
Textbook Question
Perform each operation. Write answers in standard form. (-12 -i) / (-2 -5i)
Textbook Question
Solve each equation using the square root property. 27 - x2 = 0
4
views
Textbook Question
Manufacturing to Specifications. A manufacturing firm wants to package its product in a cylindrical container 3 ft high with surface area 8π ft2. What should the radius of the circular top and bottom of the container be? (Hint: The surface area consists of the circular top and bottom and a rectangle that represents the side cut open vertically and unrolled.)
Textbook Question
Solve each inequality. Give the solution set in interval notation. -5<5+2x<11
2
views