Rational and Irrational Numbers

The video tutorial explores the properties of rational and irrational numbers through division, multiplication, and addition. It begins by demonstrating that the division of two rational numbers results in a rational number. The tutorial then examines the division of irrational numbers, showing that the result can be either rational or irrational. It further explains that multiplying a rational number by an irrational number yields an irrational result. Finally, the video discusses how adding a rational number to an irrational number results in an irrational number, providing intuitive examples to illustrate these concepts.

What is the result of dividing two rational numbers?

• Sometimes rational, sometimes irrational

• Always rational

• Cannot be determined

• Always irrational

If A and B are irrational numbers, what can be said about A/B?

• A/B is always irrational

• A/B is always rational

• A/B can be either rational or irrational

• A/B is always zero

Which of the following is an example of a rational result from dividing two irrational numbers?

• √2 / √3

• 2√2 / √2

• √5 / √7

• √3 / √5

What happens when you multiply a rational number by an irrational number?

• The result is always rational

• The result can be either rational or irrational

• The result is always zero

• The result is always irrational

Why is the square root of 8 considered irrational?

• It is less than 3

• It is a whole number

• It cannot be expressed as a fraction of two integers

• It is a perfect square

What is the result of adding a rational number to an irrational number?

• Always rational

• Always irrational

• Sometimes rational, sometimes irrational

• Always zero

If a is an irrational number, what is the nature of -4 + a?

• Irrational

• Undefined

• Rational

• Zero

Which of the following expressions is irrational?

• √4 + 1

• 3 + 2

• -4 + π

• 5 - 3

What is the result of adding -4 to the square root of 2?

• A negative integer

• Zero

• An irrational number

• A rational number

Which statement is true about the sum of a rational and an irrational number?

• It can be either rational or irrational

• It is always zero

• It is always irrational

• It is always rational