Which of the following statements is/are correct?
Statement I: The sum of a rational number and an irrational number is an irrational number.
Statement II: Negative of an irrational number is a rational number.
Statement III: The product of a non-zero rational number and an irrational number is an irrational number.

Only I

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Only I and III

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I, II and III

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Only II

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Solution

The correct option is B Only I and III
If a is a rational number and b is an irrational number, then a + b is an irrational number.
Thus, statement I is correct.
Negative of an irrational number is an irrational number.
Thus, statement II is incorrect.
The product of a non-zero rational number and an irrational number is an irrational number.
Thus, statement III is correct.

Hence, the correct answer is option (b).

Suggest Corrections

Similar questions

State, in each case, whether the given statement is true or false.

(i) The sum of two rational numbers is rational.

(ii) The sum of two irrational numbers is irrational.

(iii) The product of two rational numbers is rational.

(iv) The product of two irrational numbers is irrational.

(v) The sum of a rational number and an irrational number is irrational.

(vi) The product of a nonzero rational number and an irrational number is a rational number.

(vii) Every real number is rational.

(viii) Every real number is either rational or irrational.

(ix) $π$ is irrational and $\frac{22}{7}$ is rational.

Which of the following is a true statement ?

(a) The sum of two irrational numbers is an irrational number.

(b) The product of two irrational numbers is an irrational number.

(d) Every real number is either rational or irrational.

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