Class 9 Maths Number Systems Operation on Real numbers

Both Rational & Irrational number satisfy

• commutative (A*B =B*A)
• associative { A*(B*C) = (A*B)*C }
• distributive { A*(B+C) =A*B +A*C } laws for addition & multiplication.

If we add, subtract, multiply & divide (except 0) two rational number, we get rational number. But this statement is not true for irrational number.

• Rational Number * Rational Number = Rational Number
• Rational Number + Rational Number = Rational Number
• Rational Number - Rational Number = Rational Number
• Rational Number / Rational Number = Rational Number
• Irrational Number * Irrational Number = May not be Irrational Number. g.: √3 * √3 = 3
• Irrational Number + Irrational Number = May not be Irrational Number. g.  (2 - √3) + √3 = 2
• Irrational Number - Irrational Number = May not be Irrational Number.  g.  √3 - √3 = 0
• Irrational Number / Irrational Number = May not be Irrational Number.  g. √3/√3 = 1
• Non 0 Rational Number * Irrational Number = Irrational Number. E.g. 2 *  √3 =  2√3
• Rational Number + Irrational Number = Irrational Number. g. 2 + √3  = 2 + √3
• Rational Number - Irrational Number = Irrational Number E.g.: 7 - √3 = 7 - √3
• Non 0 Rational Number / Irrational Number = Irrational Number 3 / √3  = √3

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