To determine which of the given numbers is irrational, let's analyze each option step by step.
(A) [tex]\( 5 \)[/tex]
The number 5 is a whole number, which is a type of rational number because it can be expressed as [tex]\(\frac{5}{1}\)[/tex].
(B) [tex]\( \sqrt{5} \)[/tex]
To check if [tex]\( \sqrt{5} \)[/tex] is rational or irrational, recall that a number is rational if it can be written as a ratio of two integers. The square root of a non-perfect square, such as [tex]\( 5 \)[/tex], cannot be expressed as a ratio of two integers. Therefore, [tex]\( \sqrt{5} \)[/tex] is an irrational number.
(C) [tex]\( \sqrt{4} \)[/tex]
The square root of 4 is 2, because [tex]\( 2^2 = 4 \)[/tex]. The number 2 is a whole number, which is a type of rational number. Hence, [tex]\( \sqrt{4} \)[/tex] is rational.
(D) [tex]\( \frac{2 \sqrt{5}}{\sqrt{5}} \)[/tex]
Simplify the expression:
[tex]\[
\frac{2 \sqrt{5}}{\sqrt{5}} = 2 \cdot \frac{\sqrt{5}}{\sqrt{5}} = 2 \cdot 1 = 2
\][/tex]
The result is 2, which is a whole number and a type of rational number.
After examining all the options, we find that the only irrational number among them is:
(B) [tex]\( \sqrt{5} \)[/tex]
