Final answer:
Every irrational number is a real number (true), but not every real number is irrational (false). The square roots of some positive integers are rational (example: the square root of 4 is 2). Number 5 can be represented on a number line by marking it at the 5th unit to the right of 0.
Step-by-step explanation:
Statements on Real and Irrational Numbers
(1) Every irrational number is a real number. True. All irrational numbers fall under the category of real numbers. Irrational numbers are real numbers that cannot be expressed as a simple fraction—meaning they are decimals that never terminate or repeat. An example of an irrational number is √2 or pi (π).
(2) Every real number is an irrational number. False. Not all real numbers are irrational. Real numbers include all the rational numbers (such as 0, -1, 1/2) and irrational numbers. The correct statement is: Some real numbers are irrational.
(3) Are the square roots of all positive integers irrational? False. While many square roots of positive integers are irrational, there are notable exceptions where the square root is a whole number, and so, rational. For example, the square root of 4 is 2, which is a rational number.
(4) Representing the number 5 on the number line. To represent 5 on a number line, draw a horizontal line, mark the points 0 and 5. Then place a point exactly at the 5th unit to the right of 0.