step 1 I want to solve the square root of x minus 3 equals 3. Since we've already got a radical isolate

Solve. x-3-√(=) 3

Name: Problem 9, Chapter 8: Elementary Algebra
Uploaded: 2022-02-03T17:26:14-08:00
Duration: 19 s
Channel: James Kiss
Description: Solve. x-3-√(=) 3

Key Concepts

Radical Equations

Radical equations are equations in which the variable appears inside a radical, most commonly a square root. Solving these equations often requires isolating the radical expression, followed by eliminating the radical by raising both sides of the equation to the appropriate power. This process can introduce additional solutions, so it is essential to verify potential solutions in the original equation.

Isolating Radical Terms

When solving equations that contain radicals, an important first step is to isolate the radical term on one side of the equation. This facilitates the process of eliminating the radical by raising both sides of the equation to a power. Isolating the radical simplifies the structure of the equation and minimizes the risk of introducing unnecessary complexity during the elimination process.

Squaring Both Sides

Squaring both sides of an equation is a common technique used to remove a square root. However, this operation is not reversible and can introduce extraneous solutions—solutions that satisfy the squared equation but not the original. It is crucial to check each solution in the original equation to ensure its validity.

Extraneous Solutions

Extraneous solutions are results obtained after manipulating an equation, particularly after squaring both sides, that do not satisfy the original equation. These inadmissible solutions often arise because certain algebraic operations, such as squaring, can enlarge the solution set. Verification of each potential solution by substitution into the original equation is therefore a necessary step.

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