Which of the following statements is true?
(a) Product of two irrational numbers is always irrational
(b) Product of a rational and an irrational number is always irrational
(c) Sum of two irrational numbers can never be irrational
(d) Sum of an integer and a rational number can never be an integer

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Solution

Since we know that the product of rational and irrational number is always an irrational. For example: Let are rational and irrational numbers respectively and their product is

Hence the correct option is.

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Similar questions

The product of two irrational numbers is

(a) always irrational

(b) always rational

(d) sometimes rational and sometimes irrational

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.

Which one of the following is correct and which one is not correct? Give reasons.

1) If 'a' is a rational number and 'b' is irrational, then a+b is irrational.

2) The product of a non-profit rational number with an irrational number is always irrational.

3) Addition of any two irrational numbers can be rational.

4) Division of any two integers is an integer.

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