Question

Given the numbers 36−−√, 44−−√, 81−−√, and 17−−√, select all of the irrational numbers.

Answer 1

The irrational numbers are
`\( √(17) \)` and
`\( √(44)` as they cannot be expressed as a simple fraction and the decimal representation is non-repeating.

To determine which numbers are irrational among
`\( √(36) \), \( √(44) \), \( √(81) \)`, and
`\( √(17) \)`, we need to understand the definition of irrational numbers.

An irrational number is a number that cannot be expressed as the quotient (fraction) of two integers, and its decimal representation neither terminates nor repeats.

Let's evaluate each of the given numbers:

1.
`\( √(36) = 6 \)` - This is a rational number because it can be expressed as
`\( (6)/(1) \)`.

2.
`\( √(44)` - This is an irrational number because it cannot be expressed as a simple fraction.

3.
`\( √(81) = 9 \)` - This is a rational number because it can be expressed as
`\( (9)/(1) \)`.

4.
`\( √(17) \)` - This is an irrational number because it cannot be expressed as a simple fraction. The square root of 17 is not a whole number, and its decimal representation goes on without repeating.