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Rational Numbers

Product of a ...

Question

Product of a rational and irrational number is always irrational.

A

True

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B

False

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Solution

The correct option is B
False

$0 \times \sqrt{2} = 0$ , which is rational

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Similar questions

Product of a non-zero rational and irrational number is always irrational

Q. The product of two irrational number is
(a) always irrational
(b) always rational
(c) always an integer
(d) sometimes rational and sometimes irrational

Q. State whether the given statement is true of false:

(i) The sum of two rationals is always rational.
(ii) The product of two rationals is always rational.
(iii) The sum of two irrationals is an irrational.
(iv) The product of two irrationals is an irrational.
(v) The sum of a rational and and irrational is irrational.
(vi) The product of a rational and an irrational is irrational.

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 product of a non-zero rational number and an irrational number is
(a) always irrational
(b) always rational
(c) rational or irrational
(d) one

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