Sum/Difference of a rational and irrational number is a rational number

True

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False

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Solution

The correct option is B
False

$2 + \sqrt{2}$ is irrational.

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Similar questions

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.

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.

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