Question

Which of the following statement is true?

Answer 1

both are irrational. pick the first option.

Answer 2

The correct option is 1.

Explanation:

If a number is defined as
`(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
`(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

`√(15)=√(3* 5)=√(3)√(5)`

Since
`√(15)` is the product of two irrational numbers
`√(3)\text{ and }√(5)`, therefore
`√(15)` is an irrational number.

`√(0.001)=\sqrt{(1)/(1000)}=(1)/(10√(10))`

If any numbers is divisible by an irrational number, then the resultant number is irrational. So,
`√(0.001)` is an irrational number.

Both
`√(15)` and
`√(0.001)` are irrational. Therefore the correct option is 1.