Question

(i) `sqrt3` is a rational number.

(ii) The rationalising factor of `sqrt3 + 1` is `sqrt3 - 1`.

विकल्प

• Only (i)

• Only (ii)

• Both (i) and (ii)

• Neither (i) nor (ii)

Answer 1

Only (ii)

Explanation:

(i) `sqrt(3)` is not a rational number; it is an irrational number.

This is because `sqrt(3)` cannot be expressed as a fraction of two integers. 

A proof by contradiction shows that if it were rational, it would imply a common factor contradicting the simplest form assumption.

Therefore, statement (i) is false.

(ii) The rationalising factor of `sqrt(3) + 1` is `sqrt(3) - 1`.

Multiplying by this conjugate removes the irrational part in the denominator or numerator since `(sqrt(3) + 1)(sqrt(3) - 1) = 3 - 1 = 2`, a rational number. 

Therefore, statement (ii) is true. 

Hence, only statement (ii) is valid.