Rational and Irrational Numbers

In this tutorial, Shane Masonette explains how to distinguish between rational and irrational numbers. He defines rational numbers as those that can be expressed as a ratio of two integers and highlights that perfect squares are always rational. The tutorial further explores non-perfect squares, which result in irrational numbers, and provides examples to illustrate these concepts. Shane concludes by identifying which set of numbers contains all rational numbers and encourages viewers to subscribe for more math tutorials.

What is the main focus of this tutorial?

• Understanding algebraic expressions

• Recognizing rational and irrational numbers

• Learning about calculus

• Studying geometric shapes

How can a rational number be expressed?

• As a difference of two integers

• As a product of two integers

• As a sum of two integers

• As a ratio of two integers

Which of the following is a characteristic of a rational number?

• It is always a whole number

• It cannot be expressed as a fraction

• It can be expressed as a ratio of two integers

• It is always a decimal

What is a perfect square?

• A number that is the square of an integer

• A number that is a cube of an integer

• A number that is always irrational

• A number that can be divided by 2

Why is the square root of 144 considered rational?

• Because it is a perfect square

• Because it is a non-terminating decimal

• Because it cannot be expressed as a ratio

• Because it is an irrational number

Which of the following is a perfect square?

• 32

• 225

• 8

• 40

What is the square root of 225?

• 17

• 16

• 15

• 14

Why is the square root of 32 considered irrational?

• It is a perfect square

• It can be expressed as a ratio

• It is a whole number

• It results in a non-terminating decimal with no pattern

Which of the following numbers is irrational?

• Square root of 121

• Square root of 169

• Square root of 8

• Square root of 100

What is the square root of 169?

• 14

• 13

• 12

• 11