Question

Which of the following is a correct statement?

• A. Sum of two irrational numbers is always irrational.
• B. Sum of a rational and irrational numbers is always an irrational number.
• C. Square of an irrational number is always a rational number.
• D. Sum of two rational numbers can never be an integer.

Answer 1

The correct option is B

Sum of a rational and irrational numbers is always an irrational number.

Statement 1: Sum of two irrational numbers is always irrational.
Example: 1) $\sqrt{2}+(-\sqrt{2})$ = 0.
2) $\sqrt{3}+\sqrt{3}=2\sqrt{3}$
From the above two examples we can say that sum of two irrationals is not always an irrational.So the given statement is false.

Statement 2: Sum of a rational and irrational number is always an irrational number.

Example: 2 + $\sqrt{3}$ is 3.732142857... which is an irrational number. So the statement is true.

Statement 3: Square of an irrational number is always a rational number.

Example: $(\sqrt[3]{33}{)}^2$ = $\sqrt[3]{39}$, which is an irrational. So, the given statement is false.

Statement 4: Sum of two rational numbers can never be an integer.

Example: 2 + 4 = 6, which is an integer. So, the given statement is false.