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mathdad
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Verify that both sides of the radical equation agree without using a calculator. See picture. How can this be done algebraically?
View attachment 7967
View attachment 7967
A radical equation is an equation that contains a variable under a radical, such as a square root or cube root. Solving a radical equation requires isolating the variable and performing operations to both sides of the equation.
Verification of radical equations is important because it ensures that the solutions obtained are valid and satisfy the original equation. It helps to check for any extraneous solutions that may have been introduced during the solving process.
To verify a radical equation, you need to substitute the solutions obtained back into the original equation and simplify. If the values satisfy the equation, then they are valid solutions. If not, then they are extraneous solutions and should be discarded.
One common mistake is forgetting to square both sides when solving a square root equation, which can introduce extraneous solutions. Another mistake is not simplifying properly after substitution, leading to incorrect solutions. It is important to double check all steps and simplify fully when verifying radical equations.
Yes, it can be helpful to isolate the radical term on one side of the equation and square both sides to eliminate the radical. It is also important to check for any restrictions on the variable, such as when the radicand cannot be negative. And always remember to verify solutions by substituting them back into the original equation!
