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Irrational Numbers

Sum/Differenc...

Question

Sum/Difference of 2 irrational number is an irrational number

A

True

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B

False

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Solution

The correct option is B
False

Not always. $\sqrt{2} + \sqrt{3}$ is an irrational number .while $(2 + \sqrt{3}) - \sqrt{3}$ is a rational number.

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Q. Give two irrational numbers so that their.
(i) sum is an irrational number.
(ii) sum is not an irrational number.
(iii) difference is an irrational number.
(iv) difference is not an irrational number.
(v) product is an irrational number.
(vi) product is not an irrational number.
(vii) quotient is an irrational number.
(viii) quotient is not an irrational number.

Q. The sum of two irrational number is an irrational number (True/False).

Q. 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 an rational number.
(vi) product is an irrational number.
(vii) quotient is a rational number.
(viii) quotient is an irrational number.

Q. Statement 1: The sum of a rational number and an irrational number may or may not be irrational.

Statement 2: The difference of two irrational numbers may or may not be irrational.

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
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(d) The sum of two irrational numbers is always an integer

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