Algebra - Irrational numbers - fundamental questions.
Test Yourself 1.
Remember: try to simplify the irrational term whenever possible.
Look for even integer powers in the terms under the square root signs.
Basic simplification. | 1. Evaluate
when a = 5 and b = 4. Answer.3. |
2. Evaluate
when a = 17 and b = 5. Answer.√264 = 16.25. |
3. What is the maximum value for x given we can evaluate?
Answer.Max is 7. |
4. What is the minimum value for x given we can evaluate ?
Answer.Minimum value for x is 8 as the result under the square root sign must be equal to or greater than 0. |
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5. Simplify . Answer.Yes - it simplifies to 6. |
6. Can you simplify the following: Answer.No!!! 25 - 49 is a negative number and you can't take the square root of a negative number. | |
7.Simplify Answer.3√2. |
8. Simpify .
Answer.90. |
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9. Which of the following are rational numbers?
Answer.Only √121 = 11 and √32/ √2 = Radic;16 = 4. |
10. Simplify .
Answer.0. |
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Addition - no simplification. | 11. Simplify
Answer.4√5. |
12. Simplify .
Answer.4√3. |
13. Simplify the following Answer.-3√10. | 14. Can you simplify the following:
? Answer.Cannot be simplified further because the irrational terms cannot be simplified or combined :-( |
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15. Simplify . Answer.5√6 + 1. | 16. Simplify the following: | |
Addition - simplification. | 17. Simplify | 18. Simplify |
19. Simplify . | 20. Simplify | |
21. Simplify . | 22. Simplify | |
Multiplication. | 23. Simplify Answer.2√3. |
24. Simplify |
25. Simplify
Answer.3/2 = 1.5. |
26. Simplify
Answer.4/11. |
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27. Simplify .
Answer.4√2. |
28. Simplify
Answer.√21. |
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Multiplication with coefficients. | 29. Simplfy . | 30.
Answer.56. |
31. Simplify fully | 32. | |
33. Simplify fully . | 34. Simplify fully . | |
Division. | 35. Simplify | 36. Simplify |
37. Simplify fully .
Answer.2√3 + √7. |
38. Simplify .
Answer.1. |
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39.
Answer.√3. |
40. Simplify fully .
Answer.2 + √5/2 - 1/√6. |
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Calculation | 41. Evaluate correct to 4 significant figures.
Answer.7.624. |
42. Evaluate correct to one decimal place.
Answer.1.0. |