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 \[\dfrac{p}{q},q\ne 0\]. 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 \[\dfrac{p}{q},q\ne 0\], such that p = 0.
We can now check the third and fourth option, we get
\[\begin{align}
  & \Rightarrow \sqrt{4}=2 \\
 & \Rightarrow \sqrt{16}=4 \\
\end{align}\]
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 \[\dfrac{p}{q},q\ne 0\]. 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 \[\dfrac{p}{q},q\ne 0\], such that p = 0.