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Operations on Rational and Irrational Numbers

The sum of a ...

Question

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

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Solution

The sum of a rational number and an irrational number always results in an irrational number.

Hence, the sum of a rational number and an irrational number is an irrational number.

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Sum of a rational and an irrational number is a/an

Sum/Difference of a rational and irrational number is a rational number

Give an example of each, of two irrational numbers whose:

(i) difference is a rational number.

(ii) difference is an irrational number.

(iii) sum is a rational number.

(iv) sum is an irrational number.

(v) product is a rational number.

(vi) product is an irrational number.

(vii) quotient is a rational number.

(viii) quotient is an irrational number.

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/are correct?
Statement I: The sum of a rational number and an irrational number is an irrational number.
Statement II: Negative of an irrational number is a rational number.
Statement III: The product of a non-zero rational number and an irrational number is an irrational number.

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