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Mathematical Statement

1)What is an ...

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1)What is an irrational number 2)what are the types of irrational numbers 3)proof of an irrational 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. 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.

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. 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.

Is difference of two irrational numbers always an irrational number?

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