MATH SOLVE

2 months ago

Q:
# Identify which of the following statement(s) is always true?Statement 1: For any positive integer n, the square root of n is irrational.Statement 2: If n is a positive integer, the square root of n is rational.Statement 3: If n is a positive integer, the square root of n is rational if and only if n is a perfect square.

Accepted Solution

A:

Answer:Statement 3Step-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.