Question

Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Answer 1

Hint: Let us find the solution by taking examples of positive integers whose square root value is rational.

Complete step by step answer:
Rational numbers: A number that can be written as a ratio of two integers. (I.e. simple fraction).
Irrational number: A number that cannot be written as a ratio of two integers.
Statement (A): No, the square roots of all positive integers are not irrational. Because we know that the square roots of all positive integers includes both rational and irrational numbers.
Statement (B): Let us take a few examples whose square root of positive integers are rational numbers.
For example
$ \Rightarrow \sqrt 4 = 2$ , here $2$ is a rational number.
$ \Rightarrow \sqrt 9 = 3$, here $3$ is a rational number.
Here are the examples whose square root values are rational numbers.
Therefore by using statement (A) and statement (B) we can say that the square root of all positive integers includes both rational and irrational numbers.

NOTE: Know the difference between rational and irrational numbers. And use proper examples to prove the given question.