Get the free Solve radical equations by raising both sides of the equation to the power

Name Date LESSON 88 Class Reteach Solving Radical Equations and Inequalities Solve radical equations by raising both sides of the equation to the power n of the index of the radical. For example,

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How to solve radical equations:

1. Identify the equation: Start by identifying the radical equation that needs to be solved. Make sure to note the specific radical involved and any other terms present in the equation.
2. Isolate the radical: To solve the equation, isolate the radical term on one side of the equation. This can be done by moving all other terms to the opposite side of the equation using appropriate algebraic steps.
3. Square both sides: If the radical is a square root (\sqrt{}), square both sides of the equation to eliminate the radical. This can also be done for other radicals by raising both sides to the appropriate power that will eliminate the radical.
4. Solve the resulting equation: After squaring both sides, you will now have a simpler equation to solve. Use algebraic techniques to simplify and solve for the variable in the equation.
5. Check for extraneous solutions: Once you find a potential solution for the equation, make sure to check if it is a valid solution by substituting it back into the original equation. Sometimes, squaring both sides of an equation can introduce extraneous solutions that do not satisfy the original equation.

Who needs to solve radical equations:

1. Students studying mathematics: Radical equations are commonly encountered in algebra courses, so students studying mathematics need to learn how to solve them. This skill is essential for understanding advanced concepts and solving more complex equations.
2. Engineers and scientists: In various fields of engineering and science, radical equations often arise when dealing with equations that involve physical quantities, such as waves or electrical circuits. Engineers and scientists need to be able to solve these equations to analyze and interpret data accurately.
3. Individuals in everyday life: Although most people may not encounter radical equations on a daily basis, having the ability to solve them can still be useful. For example, when calculating the length of a diagonal in a room or determining the interest earned on investments, solving radical equations can help in making accurate calculations.

Overall, anyone seeking to understand and work with mathematical equations, whether in academic settings or practical applications, needs to know how to solve radical equations.

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