Option A:
are irrational numbers.
Solution:
Given numbers:
![$\sqrt{17} , 0, \sqrt[3]{8} , \frac{22}{7} , \sqrt{81} , \sqrt[3]{14}](https://tex.z-dn.net/?f=%24%5Csqrt%7B17%7D%20%2C%200%2C%20%5Csqrt%5B3%5D%7B8%7D%20%2C%20%5Cfrac%7B22%7D%7B7%7D%20%2C%20%5Csqrt%7B81%7D%20%2C%20%5Csqrt%5B3%5D%7B14%7D)
To which of these are irrational numbers:
<u>Irrational:</u>
An irrational number cannot be written in the form
, where a and b are integers and b is non-zero.
(1)
cannot be written as
.
So, it is a irrational.
(2) ![\sqrt[3]{8} =\sqrt[3]{2^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%20%3D%5Csqrt%5B3%5D%7B2%5E3%7D)
Cube and cube roots are get canceled.
![\sqrt[3]{8} =2](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B8%7D%20%3D2)
2 is an integer. So it is not a irrational number.
(3)
is in the form
.
So it is not a irrational number.
(4)
Square and square root are get canceled.

9 is an integer. So it is not a irrational number.
(5) ![\sqrt[3]{14}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B14%7D)
14 cannot be written as
form.
So, it is a irrational number.
Therefore
are irrational numbers.
Option A is the correct answer.