Question

Which of these numbers are irrational?see in picture for answer choices ​

Answer 1

Option A:

$\sqrt{17}, \sqrt[3]{14}$ are irrational numbers.

Solution:

Given numbers:

$\sqrt{17} , 0, \sqrt[3]{8} , \frac{22}{7} , \sqrt{81} , \sqrt[3]{14}$

To which of these are irrational numbers:

Irrational:

An irrational number cannot be written in the form $\frac{a}{b}$, where a and b are integers and b is non-zero.

(1) $\sqrt{17}$ cannot be written as $\frac{a}{b}$.

So, it is a irrational.

(2) $\sqrt[3]{8} =\sqrt[3]{2^3}$

Cube and cube roots are get canceled.

$\sqrt[3]{8} =2$

2 is an integer. So it is not a irrational number.

(3) $\frac{22}{7}$ is in the form $\frac{a}{b}$.

So it is not a irrational number.

(4)$\sqrt{81}=\sqrt{9^2}$

Square and square root are get canceled.

$\sqrt{81}=9$

9 is an integer. So it is not a irrational number.

(5) $\sqrt[3]{14}$

14 cannot be written as $\frac{a}{b}$ form.

So, it is a irrational number.

Therefore $\sqrt{17}, \sqrt[3]{14}$ are irrational numbers.

Option A is the correct answer.