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Q.

State whether the given statement is true or false.

Sum of two irrational number is always irrational.

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a

True

b

False

answer is A.

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Detailed Solution

The given statement is that the sum of two irrational numbers will be an irrational number.
Here, we have to state if the given statement is true or not.
As per the properties of addition in case of real numbers, we know that all real numbers are closed under addition.
Now, as real numbers also include irrational numbers, so we conclude that all irrational numbers are also closed under addition.
This means that if we add to irrational numbers, then the sum thus obtained will also be irrational.
Example: Adding

2

and

3

, which are two irrational numbers, gives the sum as

(2 + 3)

, which is also irrational.
Hence, the statement is true.
So, the correct option is 1.

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