Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

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.
  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.
  9. Which of the following are rational numbers?


Answer.Only √121 = 11 and
√32/ √2 = Radic;16 = 4.		 10. Simplify .
Answer.0.
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 :-(
  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.
  27. Simplify .
Answer.4√2.		 28. Simplify
Answer.√21.
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.
  39.
Answer.√3.		 40. Simplify fully .
Answer.2 + √5/2 - 1/√6.
Calculation 41. Evaluate correct to 4 significant figures.
Answer.7.624.		 42. Evaluate correct to one decimal place.
Answer.1.0.