Is it true that the sum of two irrational numbers is an irrational number?

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True

False

answer is B.

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Detailed Solution

Given to find sum of two irrational numbers is an irrational number or not.
Rational numbers are those that can be represented as p/q where p, q are integers and q is not equal to zero.
A real number that cannot be expressed as a ratio of integers is an irrational number.
An irrational number's decimal expansion is neither terminating nor recurring.
Let

(p + q) and (p − q)

be two irrational numbers, with both p and q are rationals and q is not a perfect square.
Add the irrational numbers,

p + q + p − q = p + p + q − q = 2 p

Given p is a rational number, and thus 2p is also a rational number.
Therefore the sum of two irrational numbers is not always an irrational number.
Thus the statement, sum of two irrational numbers is an irrational number is false.
Hence the correct option is 2.

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