Q.

Is it true that the sum of two irrationals is always irrational?


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a

True

b

False 

answer is B.

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Detailed Solution

Given that, the sum of two irrationals is always irrational.
Assume that the numbers 5+3 2   and 3 2  are irrational.
If we add the two irrational integers,
⇒5+3 2 +3 2 ⇒5+6 2  
The final value 5+6 2   cannot be expressed as a simple fraction.
The number which cannot be expressed in fractional form p q   is an irrational number.
Also, if we take 5+3 2  , −3 2   and add them.
⇒5+3 2 −3 2 ⇒5  
5 is a rational number.
So, the sum of irrationals may or may not be rational.
Hence, the given statement is false and the correct answer is the sum of two irrationals is not always irrational.
Therefore, option 2 is correct.
 
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