Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
1. Equations & Inequalities
The Square Root Property
3:09 minutes
Problem 32
Textbook Question
Textbook QuestionSolve each equation using the square root property. See Example 2. (4x + 1)^2 = 20
Verified Solution
This video solution was recommended by our tutors as helpful for the problem above
Video duration:
3mPlay a video:
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 a squared expression equals a number, then the original expression can be solved by taking the square root of both sides. Specifically, if (a)^2 = b, then a = ±√b. This property is essential for solving quadratic equations and allows for finding the values of the variable involved.
Recommended video:
02:20
Imaginary Roots with the Square Root Property
Isolating the Squared Term
To effectively use the square root property, it is crucial to isolate the squared term on one side of the equation. In the given equation (4x + 1)^2 = 20, we first ensure that (4x + 1)^2 is alone on one side before applying the square root property. This step is vital for correctly applying the property and finding the correct solutions.
Recommended video:
06:24
Solving Quadratic Equations by Completing the Square
Handling ± Solutions
When applying the square root property, it is important to remember that taking the square root of a number yields both a positive and a negative solution. For example, if we find that (4x + 1) = ±√20, we must consider both cases: 4x + 1 = √20 and 4x + 1 = -√20. This ensures that all possible solutions to the equation are accounted for.
Recommended video:
5:34
Shifts of Functions
Watch next
Master Solving Quadratic Equations by the Square Root Property with a bite sized video explanation from Callie
Start learning