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Operations on Rational and Irrational Numbers

What can you ...

Question

What can you say about the sum of a rational number and an irrational number?

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Solution

Sum of a rational number and an irrational number is an irrational number.
Example: 4 + $\sqrt{5}$ represents sum of rational and an irrational number where 4 is rational and $\sqrt{5}$ is irrational.

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

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