Here are the essential concepts you must grasp in order to answer the question correctly.
Radical Equations
Radical equations are equations that involve a variable within a radical (square root, cube root, etc.). To solve these equations, one typically isolates the radical on one side and then squares both sides to eliminate the radical. This process may introduce extraneous solutions, so it's essential to check all potential solutions in the original equation.
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Isolating the Radical
Isolating the radical is a crucial step in solving radical equations. This involves rearranging the equation so that the radical expression is alone on one side. Once isolated, squaring both sides of the equation can simplify the problem, allowing for further algebraic manipulation to find the variable's value.
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Extraneous Solutions
Extraneous solutions are solutions that emerge from the algebraic manipulation of an equation but do not satisfy the original equation. When solving radical equations, squaring both sides can introduce these false solutions. Therefore, it is vital to substitute any found solutions back into the original equation to verify their validity.
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Categorizing Linear Equations