POLQ 2 | Lesson 3 | Practice (Solving Radical Equations)

Solving Radical Equations

Try the following radical equations. Make sure to check each solution to be sure it makes the original equation true.

a) \( \sqrt{x} =7 \)

b) \( \sqrt{x} =-7 \)

c) \( \sqrt[3]{x} =7 \)

d) \( \sqrt[3]{x} =-7 \)

e) \(\sqrt{x}-1 = \sqrt{x}\)

f)  \(\sqrt{x-15} = \sqrt{x}-3\)

The solutions that did not “work” are called extraneous solutions.

Notice that in b) the right hand side of the equation is positive, you are taking the positive square root of \(x\).  Why does d) have a) solution and b) does not?

Check your solutions. 

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