Question

Which of the following statement is true?

Answer 1

Both are irrational. pick the first option.

Answer 2

Answer:

The correct option is 1.

Step-by-step explanation:

If a number is defined as $\frac{p}{q}$, where p and q are distinct integers and q≠0, then it is called a rational number.

For example: 0.2, 3/4, 5%.

If a number can not be defined as $\frac{p}{q}$, where p and q are integers and q≠0, then it is called an irrational number.

For example: √2, √3, √(0.3).

The given numbers can be written as

$\sqrt{15}=\sqrt{3\times 5}=\sqrt{3}\sqrt{5}$

Since $\sqrt{15}$ is the product of two irrational numbers $\sqrt{3}\text{ and }\sqrt{5}$, therefore $\sqrt{15}$ is an irrational number.

$\sqrt{0.001}=\sqrt{\frac{1}{1000}}=\frac{1}{10\sqrt{10}}$

If any numbers is divisible by an irrational number, then the resultant number is irrational. So, $\sqrt{0.001}$ is an irrational number.

Both $\sqrt{15}$ and $\sqrt{0.001}$ are irrational. Therefore the correct option is 1.