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Name Date Radical Equations 10.3 Solving Exploration 10.3 For use with Essential Question How can you solve an equation that contains square roots? 1 EXPLORATION: Analyzing a Free-falling Object Go
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How to fill out radical equations:

01
Identify the radical: Look for the square root (√), cube root (∛), or any other root symbol in the equation. This will help you determine the type of radical equation you are dealing with.
02
Isolate the radical: Move any terms or constants to the other side of the equation, leaving only the radical on one side. This will make it easier to solve for the variable within the radical.
03
Square both sides: If the radical is a square root, you can eliminate it by squaring both sides of the equation. This will help you get rid of the radical sign and simplify the equation into a quadratic form.
04
Solve for the variable: Once you have squared both sides and eliminated the radical, you can solve the resulting equation for the variable. Use algebraic techniques like factoring, completing the square, or the quadratic formula to find the solutions.
05
Check for extraneous solutions: After solving for the variable, substitute the solution back into the original equation to check if it satisfies the equation. Sometimes, during the process of squaring both sides, extraneous solutions may appear, so it is important to verify the validity of the obtained solutions.

Who needs radical equations:

01
Students studying advanced mathematics: Radical equations are often encountered in higher-level mathematics courses. Understanding how to solve them is crucial for success in these subjects, such as algebra, trigonometry, or calculus.
02
Engineers and scientists: Radical equations frequently arise in various engineering and scientific fields. These equations are used to model and solve real-world problems in physics, electrical engineering, and other scientific disciplines.
03
Individuals working with geometry or measurements: Radical equations often appear in geometry problems, especially when dealing with lengths, areas, or volumes. Knowing how to solve these equations is valuable when solving geometric problems or calculating measurements accurately.
04
Anyone interested in problem-solving: Radical equations provide an excellent opportunity to develop critical thinking and problem-solving skills. Learning how to tackle these equations can enhance logical reasoning abilities, allowing individuals to approach different types of problems with a systematic approach.
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Radical equations are equations that contain radicals, such as square roots or cube roots, involving variables.
Anyone dealing with mathematical equations and calculations may need to work with radical equations.
When filling out radical equations, solve for the variable inside the radical first, then isolate the variable to find the solution.
Radical equations are used to solve problems involving square roots or other types of radicals, helping to find solutions to mathematical equations.
The variables involved in the equation, the radical expressions, and the solutions to the equations must be reported.
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