If we take the sum of an irrational number and a rational number, which of the following options holds true regarding the resulting sum?

It may be irrational.

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It is always irrational.

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It is always rational.

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It may be natural.

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Solution

The correct option is B
It is always irrational.

The decimal representation of an irrational number is non-terminating and non-recurring, and the decimal representation of a rational number is either terminating or non-terminating recurring. Adding both of them, we always get a non-terminating and non-recurring decimal. Hence, it is always irrational.

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Similar questions

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.

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.

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