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How to Solve a Radical Equation
To solve an equation that contains a variable under a square root, follow a four-step procedure:
Step 1. Isolate the radical on one side of the equation. If the square root expression is not already by itself, use addition, subtraction, or other algebraic operations to move all other terms to the opposite side.
Step 2. Square both sides of the equation. Applying the Squaring Property of Square Roots removes the radical from the isolated side, converting the equation into a standard polynomial equation.
Step 3. Solve the new equation. Use appropriate algebraic techniques (such as combining like terms, factoring, or applying properties of equality) to find the value(s) of the variable.
Step 4. Check the answer. Substitute each candidate solution back into the original radical equation and verify that it produces a true statement. Any value that does not satisfy the original equation is an extraneous solution and must be discarded.
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Elementary Algebra @ OpenStax
Ch.9 Roots and Radicals - Elementary Algebra @ OpenStax
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A safety inspector is using a formula that contains a square root to determine the maximum load for a warehouse shelf. To solve for the unknown variable, the inspector must follow a specific algebraic procedure. Arrange the following steps in the correct order to solve a radical equation.
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