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Standard IX

Mathematics

Irrational Numbers

The product o...

Question

The product of two irrational numbers is ____.

irrational

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rational

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rational or irrational

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whole

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Solution

The correct option is C rational or irrational
Product of an irrational and an irrational number can be rational or irrational.

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Similar questions

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

State, in each case, whether the given statement is true or false.

(i) The sum of two rational numbers is rational.

(ii) The sum of two irrational numbers is irrational.

(iii) The product of two rational numbers is rational.

(iv) The product of two irrational numbers is irrational.

(v) The sum of a rational number and an irrational number is irrational.

(vi) The product of a nonzero rational number and an irrational number is a rational number.

(vii) Every real number is rational.

(viii) Every real number is either rational or irrational.

(ix) $π$ is irrational and $\frac{22}{7}$ is rational.

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.

Which of the following is a true statement ?

(a) The sum of two irrational numbers is an irrational number.

(b) The product of two irrational numbers is an irrational number.

(d) Every real number is either rational or irrational.

The product of two irrational numbers is

(a) always irrational

(b) always rational

(d) sometimes rational and sometimes irrational

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The product of two irrational numbers is ____.

The correct option is C rational or irrationalProduct of an irrational and an irrational number can be rational or irrational.

The correct option is C rational or irrational
Product of an irrational and an irrational number can be rational or irrational.