Question

4. Which of the following given statement(s) is/are correct? a) The sum or difference of a rational number and an irrational number is irrational. b) The product or quotient of a non-zero rational number with an irrational number is irrational. c) If we add, subtract, multiply or divide two irrationals, the result may be rational or irrational answer fast

Answer 1

Answer:

(c)..........is the correct answer

Answer 2

All the three statements are correct.

• If a is rational number and b is irrational number, then a + b must also be irrational. Similar is when there is subtraction of rational and irrational number. For example, 6 is rational number$\sqrt 6$ is irrational number so their addition will be 6 + $\sqrt6$ which is an irrational number.  As a result, assertion a is true.

• An irrational number is the result of adding a non-zero rational number to an irrational number. As a result, statement b is also true.
• If we multiply $\sqrt6$ by $\sqrt6$, the result will be 6 which is a rational number while we add these two, the result will be 2$\sqrt6$, which is an irrational number so the result can be rational or irrational, hence third statement is also true.

Hence, all the three statements are correct.

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