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is an irrational number. also, check whether is rational or irrational.

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Irrational

Rational

Both a and b

None of these

answer is B.

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Detailed Solution

Concept- Consider the expression

as rational, so it is equal to p/q. Thus, simplify the terms and find if the expression thus obtained is rational or not. If not then it’s irrational.
Let us assume that is a rational number.
Let P=

Is rational
On squaring both sides we get

….(i)
Since P is a rational number, therefore,

is also rational and

Is also rational.
But

is irrational and in equation (i)

Rational

Irrational
Hence, our assumption is incorrect and

is an irrational number.

Hence, P is rational

and both p and q are coprime numbers.
Hence, the correct option is 2.

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