Irrational Numbers and Square Roots

The video tutorial covers the concept of irrational numbers, explaining that they cannot be expressed as a ratio of two integers or as a repeating or terminating decimal. Examples like pi and the square root of 2 are discussed. The tutorial also covers how to approximate irrational numbers as decimals and compare real numbers using symbols for less than, greater than, or equal to. It explains using perfect squares to estimate square roots and balancing equations involving square roots. The lesson concludes with a comparison of differences using subtraction and square roots, and a brief introduction to the next part of the lesson.

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

• 0.75

• 3/4

• Pi

• 2

How can we approximate irrational numbers for comparison?

• By using fractions

• By using repeating decimals

• By using perfect squares

• By using whole numbers

What is the square root of 64?

• 8

• 9

• 7

• 6

If 3 plus the square root of 7 equals the square root of 7 plus a number, what is that number?

• 1

• 2

• 4

• 3

What is the square root of 16?

• 2

• 4

• 3

• 5

Between which two integers does the square root of 75 lie?

• 8 and 9

• 10 and 11

• 9 and 10

• 7 and 8

What is the approximate value of the square root of 8?

• 2.5

• 2.7

• 2.9

• 3.1

Which is greater: the difference between 8 and 2, or the difference between the square root of 8 and the square root of 2?

• Square root of 8 - Square root of 2

• Both are equal

• 8 - 2

• Cannot be determined

What is the square root of 9?

• 2

• 3

• 4

• 5

What is the approximate value of the square root of 2?

• 1.5

• 1.2

• 1.4

• 1.3