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If and and are two distinct irrational numbers, then which of the following is always an irrational number.

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p q

answer is D.

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Detailed Solution

Concept- Given P and q are irrational numbers which implies they are not rational. Irrational numbers are repeating decimals, square roots, or cube roots that cannot be expressed as rational numbers.Let

and

(as they are distinct) . So, apply the operations on p and q as specified in the options to determine which remains an irrational number.
As, given

and

are two distinct irrational numbers.
Let

and

Then,
Option 1
Question Image

Option 2

Option 3

Option 4

which is an irrational number as we know that the sum of rational and irrational is always irrational.
Hence, the correct Option is (4) .

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