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

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.
  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.
38.
  39. 40.
Calculation 41. 42.