The sum of two irrational numbers is an irrational numbers(True/False). Give reason for your answer.

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Solution

False
Sum of two irrational numbers can be rational if the irrational parts have the sum as zero so the result is rational.
For example,
$\sqrt{3}$ and − $\sqrt{3}$
The sum is 0, which is a rational number.

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Similar questions

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

Q. Give an example of two irrational numbers, whose sum is an irrational number.

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.

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.

Let $x$ be a rational number and $y$ be an irrational number. Is $x + y$ necessarily an irrational number ? Give an example in support of your answer.

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The sum of two irrational numbers is an irrational numbers(True/False). Give reason for your answer.

FalseSum of two irrational numbers can be rational if the irrational parts have the sum as zero so the result is rational.For example, √3 and −√3 ​The sum is 0, which is a rational number.

False
Sum of two irrational numbers can be rational if the irrational parts have the sum as zero so the result is rational.
For example,
$\sqrt{3}$ and − $\sqrt{3}$
The sum is 0, which is a rational number.