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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
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Q. Which of the following statements is true?
(a) Product of two irrational numbers is always irrational
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(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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