Radical operations questions
- 2. Radical Expressions are called common if their radicands, the terms under the radical sign, have the same value. Common Radicals Not Common Radicals 4 3 and 5 3 4 3 and 4 5
- 3. Question 1: Mari and Justin’s math teacher put two radical expressions on the board, 3 10 and 5 2 + 8 Mari said the two expressions were common radical expressions but Justin disagreed. Who is correct? Explain why they are correct.
- 5. Radical expressions with common radicals can be added or subtracted. Example:
- 6. Question 2: Add 3 10 + 5 10
- 8. Radical expressions without common radicals cannot be added or subtracted. Example: However, sometimes radical expressions without common radicals become common radicals when simplified. Example:
- 9. Question 3: Subtract 90 − 3 10
- 10. Question 4: Agent J and Agent K ran into Zargar from planet Zultar. Zargar said that since 𝑥 and 𝑦 can be any number then, 2 𝑥 + 3 𝑦 = 5 𝑥 + 𝑦 Is Zargar correct? Explain why or why not.
- 12. Unlike adding and subtracting radical expressions, you do not need common radicals to multiply or divide radical expressions. To multiply, you simply multiply the numbers outside the radical together and then multiply the numbers inside the radical. Example:
- 13. Question 5: Multiply, 6 2 ∙ 3 5
- 15. Sometimes when you multiple two radical expressions perfect square factors are the result. For that reason, it is usually best when combining the numbers in the radical to leave them factored until the very end. Example,
- 16. Question 6: Carmen multiplied 5 together with another radical and got a result whose radical was 2. Lynn said that was impossible. Who is right? Show that you are right saying who is right.
- 18. Similar to multiplying radicals, to divide you simply divide the numbers outside the radical and then divide the numbers inside the radical. Example:
- 19. If a radical remains in the denominator, you rationalize the denominator as follows, 𝑥 + 1 𝑥 = 𝑥 + 1 𝑥 ∙ 𝑥 𝑥 = 𝑥(𝑥 + 1) 𝑥2 = 𝑥 𝑥 + 1 𝑥
- 20. Question 7: When would you rationalize the denominator?