Rational and Irrational Numbers

This video tutorial covers the concept of irrational numbers, explaining how they differ from rational numbers. It provides methods for classifying real numbers, offers examples of both rational and irrational numbers, and demonstrates how to approximate irrational numbers. The tutorial also includes a comparison of irrational numbers and practical applications such as calculating distances using the Pythagorean theorem and a periscope.

Which of the following is an example of an irrational number?

• 0.75

• Square root of 2

• 3.14

• 1/2

What is a characteristic of a rational number?

• It cannot be expressed as a fraction.

• It is always a whole number.

• Its decimal form neither terminates nor repeats.

• It can be expressed as a ratio of two integers.

Which of the following numbers is irrational?

• Square root of 16

• Pi

• 0.333...

• Cube root of 8

What is the approximate integer value of the square root of 71?

• 10

• 7

• 9

• 8

To the nearest tenth, what is the square root of 71?

• 8.1

• 8.4

• 8.2

• 8.3

Which is greater: the square root of 35 or the cube root of 81?

• Cannot be determined

• They are equal

• Cube root of 81

• Square root of 35

What is the cube root of 64?

• 3

• 4

• 5

• 6

Using the Pythagorean theorem, what is the distance between the points (-4, -3) and (3, -5)?

• 8.0

• 5.0

• 7.3

• 6.5

If a periscope is 3 feet above water, approximately how far can it see in nautical miles?

• 2.5

• 1.5

• 3.0

• 2.0

What is the square root of 53 approximately?

• 7.3

• 7.2

• 7.4

• 7.1