# Lesson Worksheet: Radical Equations Mathematics

In this worksheet, we will practice solving equations that include radical expressions, where the variable is the radicand, by raising each side to a power.

Q1:

The natural way to solve introduces an extraneous solution. What is that extraneous solution?

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• E

Q2:

Solve .

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• D

Q3:

Solve .

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Q4:

Find the value of given that .

Q5:

Find the solution set of the equation , given that .

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Q6:

Find the value of for which .

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Q7:

Given that , find the value of .

Q8:

For what value of is introduced as an extraneous solution to the equation when it is solved in the natural way?

Q9:

In order to solve the equation , Daniel started with

What solutions did Daniel find?

Q10:

What is the solution set of the equation ?

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Q11:

Solve .

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Q12:

Find the value of given that .

Q13:

Solve .

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Q14:

Find the solution set of in .

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Q15:

Solve .

Q16:

Solve .

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Q17:

Consider the following argument for solving :

1. .

• Asquaring does not give 9
• Bnot checking for extraneous solutions

Q18:

Find the solution set of the equation given that .

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Q19:

Solve .

Q20:

Given that , find the value of .

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Q21:

Solve .

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Q22:

Daniel starts to solve as follows:

Finish the solution for him.

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Q23:

Squaring both sides of introduces an extraneous solution. What is that extraneous solution?

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• E

Q24:

What is the solution set of ?

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Q25:

Given that , find the value of .

• A11
• B
• C0
• D22
• E33