Practice quiz: Solving radical equations with two radicals for Algebra 2

📚 Topic Summary

Solving radical equations with two radicals involves isolating one radical, squaring both sides to eliminate it, and then repeating the process for the second radical. This often leads to a polynomial equation that you can solve using standard algebraic techniques. Always remember to check your solutions in the original equation to avoid extraneous roots!

When dealing with two radicals, strategic isolation is key. Aim to isolate the more complex radical first to simplify the subsequent steps. Squaring both sides introduces the possibility of extraneous solutions, so meticulous checking is essential for accuracy.

🧠 Part A: Vocabulary

Match the terms with their definitions:

1. Radical Equation
2. Extraneous Solution
3. Isolate
4. Square Root
5. Index

Definitions:

1. A solution that appears valid but does not satisfy the original equation.
2. The small number indicating the degree of the root.
3. To set apart or separate from others.
4. An equation containing a variable within a radical symbol.
5. A number that, when multiplied by itself, equals a given number.

Answer Key:

• 🔍 Radical Equation: An equation containing a variable within a radical symbol.
• 💡 Extraneous Solution: A solution that appears valid but does not satisfy the original equation.
• 📝 Isolate: To set apart or separate from others.
• ➗ Square Root: A number that, when multiplied by itself, equals a given number.
• ⚗️ Index: The small number indicating the degree of the root.

✍️ Part B: Fill in the Blanks

When solving radical equations with two radicals, the first step is to ______ one of the radicals. Then, you ______ both sides of the equation. After simplifying, ______ the process for the remaining radical. Finally, it's crucial to ______ your solutions to check for ______ solutions.

Answer Key:

• 🔍 Isolate
• 💡 Square
• 📝 Repeat
• ➗ Check
• ⚗️ Extraneous

🤔 Part C: Critical Thinking

Explain why it is important to check for extraneous solutions when solving radical equations, and provide an example of how an extraneous solution might arise.