Answer:
Statement 3
Step-by-step explanation:
Statement 1: For any positive integer n, the square root of n is irrational.
Suppose n = 25 (25 is positive integer), then
[tex]\sqrt{n}=\sqrt{25}=5[/tex]
Since 5 is rational number, this statement is false.
Statement 2: If n is a positive integer, the square root of n is rational.
Suppose n = 8 (8 is positive integer), then
[tex]\sqrt{n}=\sqrt{8}=2\sqrt{2}[/tex]
Since [tex]2\sqrt{2}[/tex] is irrational number, this statement is false.
Statement 3: If n is a positive integer, the square root of n is rational if and only if n is a perfect square.
If n is a positive integer and square root of n is rational, then n is a perfect square.
If n is a positive integer and n is a perfect square, then square root of n is a rational number.
This statement is true.
