Question

Which one of the following is not a rational number?
A. $$\sqrt{2}$$
B. 0
C. $$\sqrt{4}$$
D. $$\sqrt{16}$$

Answer 1

Hint: In this problem, we have to find the irrational number from the given options. We know that rational numbers are any numbers which can be written in the form of $${\displaystyle \frac{p}{q}},q\ne 0$$. We also know that an irrational number is a non-terminating or non-repeating number and has decimal expansion. Here we can check the given root values for irrational numbers to get the required answer.

Complete step-by-step answer:
Here we have to find the irrational number from the following options.
A. $$\sqrt{2}$$
B. 0
C. $$\sqrt{4}$$
D. $$\sqrt{16}$$
We can now check the root value of each option.
We can now take the first option, we get
$$\Rightarrow \sqrt{2}=1.41421356...$$
We can see that the value of $$\sqrt{2}$$ is non-termination and has a decimal expansion, hence it is an irrational number.
We can see that 0 is a rational number, where in the form of $${\displaystyle \frac{p}{q}},q\ne 0$$, such that p = 0.
We can now check the third and fourth option, we get
$$\begin{array}{rl}& \Rightarrow \sqrt{4}=2\\ & \Rightarrow \sqrt{16}=4\end{array}$$
Here, we can see that the last two options are rational numbers.

So, the correct answer is “Option A”.

Note: We should always remember that rational numbers are any numbers which can be written in the form of $${\displaystyle \frac{p}{q}},q\ne 0$$. We also know that an irrational number is a non-terminating or non-repeating number and has decimal expansion. We should also remember that 0 is a rational number, where in the form of $${\displaystyle \frac{p}{q}},q\ne 0$$, such that p = 0.