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Operations on Rational and Irrational Numbers

The sum of a ...

Question

The sum of a rational and irrational number is always an irrational number.

A

False

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B

True

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Solution

The correct option is B True

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Q. Which one of the following statements is true?
(a) The sum of two irrational numbers is always an irrational number
(b) The sum of two irrational numbers is always a rational number
(c) The sum of two irrational numbers may be a rational number or an irrational number
(d) The sum of two irrational numbers is always an integer

Q. Prove that the sum of a rational number and an irrational number is always irrational.

If we take the sum of an irrational number and a rational number, resulting sum is always irrational.

Q. 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

Q. The product of a non-zero rational number and an irrational number is
(a) always irrational
(b) always rational
(c) rational or irrational
(d) one

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