Question

Is the square root of $4$ is rational or irrational?

Answer 1

Hint: Here we will first take one example of the positive integer whose square root value will give a rational number. To check whether the square root of a number is rational or not we must check whether the number is a perfect square or not. We can easily see that $4$ is a perfect square of $2\,or\, - 2$.

Complete step-by-step solution:
Rational number is defined as a number that can be expressed as a ratio of two integers or can be expressed as a fraction.
Irrational number is defined as a number that cannot be expressed as the ratio of two integers.
The square roots of all positive integers are not irrational because we know that the square roots of all positive integers include both rational and irrational numbers.
Let’s take a positive integer $4$. Taking square root of $4$, we get
$ \Rightarrow \,\sqrt 4 \, = \,2$
We know 2 is a rational number.
Therefore, the square root of $4$ is a rational number.

Note: Here in this question, we require the knowledge of rational and irrational numbers. We need to keep in mind that the rational includes only those decimal numbers which are recurring in nature whereas irrational includes only those decimal numbers which are non-recurring in nature or non-terminating in nature. The numerator and denominator of a rational number can be whole numbers, integers, etc. Every integer can be a rational number however not every rational number can be an integer.