If we add, subtract, multiply or divide two irrational numbers, the result may be a _____ number or an irrational number.

Open in App

Solution

Solving for two irrational numbers:
If we add, subtract, multiply or divide two irrational numbers, the resultant number will always be a real number.
i.e., it can be rational or irrational.
Example: Let, $2 + \sqrt{3} a n d 2 - \sqrt{3}$ be two irrational numbers.
Sum of irrational numbers:
$= (2 + \sqrt{3}) + (2 - \sqrt{3}) = 2 + \sqrt{3} + 2 - \sqrt{3} = 4 [i s r a t i o n a l]$
Subtract of irrationals:
$= (2 + \sqrt{3}) - (2 - \sqrt{3}) = 2 + \sqrt{3} - 2 + \sqrt{3} = 2 \sqrt{3} [i s i r r a t i o n a l]$
Product of irrationals:
$= (2 + \sqrt{3}) (2 - \sqrt{3}) = 2^{2} - {(\sqrt{3})}^{2} = 4 - 3 = 1 [i s i r r a t i o n a l]$
Quotient of irrationals:
$\frac{(2 + \sqrt{3})}{(2 - \sqrt{3})} = \frac{(2 + \sqrt{3})}{(2 - \sqrt{3})} \times \frac{(2 + \sqrt{3})}{(2 + \sqrt{3})} [b y r a t i o n a l i s a t i o n] = \frac{4 + 3 + 4 \sqrt{3}}{4 - 3} = 7 + 4 \sqrt{3} [i s i r r a t i o n a l]$
Hence, if we add, subtract, multiply or divide two irrational numbers, the result may be a rational number or an irrational number.

Suggest Corrections

Similar questions

When we divide two irrational numbers, we may or may not get a rational number.

When we divide two irrational numbers we may or may not get a rational number

Join BYJU'S Learning Program