Algebra - Irrational numbers - fundamental questions.
Test Yourself 1 - Solutions.
Remember: try to simplify the irrational term whenever possible.
Answer to 2 decimal places when an integer is not the answer.
Look for integer powers which are even in the terms under the square root signs.
Basic simplification. | 1. | 2. |
3. - The largest value is when x = 0. Hence 7. | 4. - the minimum value for x is 8 which sets the expression = 0. 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. ALWAYS remember to consider the plus and minus signs when taking a square root. | 6. cannot be simplified and has no solution because 25 - 49 < o and so we cannot take the square root. | |
7. | 8. = 32 × 10 = 90. | |
9. A rational number is a number which can be expressed as a ratio of two integers. | 10. | |
Addition - no simplification. | 11. | 12. |
13. | 14. | |
15. Note: not all terms combine. |
16. | |
Addition - simplification. | 17. | 18. |
19. | 20. | |
21. | 22. | |
Multiplication. | 23. | 24. |
25. | 26. | |
27. | 28. | |
Multiplication with coefficients. | 29. | 30. |
31. | 32. | |
33. | 34. | |
Division. | 35. | 36. |
37.
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38. | |
39. | 40. | |
Calculation | 41. | 42. |