Question

Product of two irrational numbers may or may not be irrational.

• A. True
• B. False

Answer 1

The correct option is A True

Rational number:

The number of the form $\frac{p}{q}$ where $p\mathrm{and}\mathrm{q}$ are integers and $q$must not be equal to 0, are known as rational numbers.

Irrational number:

The number can not be represented in the form $\frac{p}{q}$ where $p\mathrm{and}\mathrm{q}$ are integers and $q$must not be equal to 0, are known as irrational numbers.

The product of two irrational numbers may or may not be irrational. This statement is true because it depends on numbers.

Example: Consider $\sqrt{5}\mathrm{and}\sqrt{2}$ then,

$\Rightarrow \sqrt{5}\times \sqrt{2}=\sqrt{10}$ Here $\sqrt{10}$ is an irrational number

Now, consider $\sqrt{8}\mathrm{and}\sqrt{2}$ then,

$$\begin{gathered} \Rightarrow \sqrt{8}\times \sqrt{2}=\sqrt{16} \\ =4 \end{gathered}$$

Here, 4 is a rational number.

Hence, the given statement is true.