Number Systems - Operations on Real Numbers

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Case 1: One number is rational and another number is an irrational
Case 2: Both the numbers are irrational
Case 3: Both the numbers are rational





Important Points:

• The sum, difference of a rational and irrational is an irrational number
  Example : 2+√3, 2-√3
• The product, quotient of a non-zero rational and irrational is an irrational number.
  Example : 2×√5, 2 ∕√5
• The sum, difference, product and quotient of two irrational numbers need not be an irrational number.