Understanding Irrational Numbers and Square Roots

The video tutorial explains irrational numbers, focusing on their non-terminating and non-repeating decimal nature. It uses examples like pi and non-perfect square roots to illustrate these concepts. The tutorial then demonstrates how to approximate square roots of numbers like twelve, ninety-seven, and fifty-seven using a calculator, emphasizing rounding to the nearest thousandth.

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

• 1/2

• 3.14

• 4

• √2

What is the approximate value of pi as a decimal?

• 3.14159

• 3.14

• 3.141

• 3.2

Which of the following statements is true about irrational numbers?

• They are always whole numbers

• They have repeating decimal patterns

• They can be expressed as a fraction

• They do not terminate or repeat

What is the key characteristic of non-perfect square roots?

• They are always greater than 10

• They are always less than 1

• They are irrational

• They are always integers

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

• 5 and 6

• 4 and 5

• 3 and 4

• 2 and 3

What is the approximate value of the square root of twelve rounded to the nearest thousandth?

• 3.465

• 3.466

• 3.467

• 3.464

Between which two integers does the square root of ninety-seven lie?

• 11 and 12

• 8 and 9

• 9 and 10

• 10 and 11

What is the approximate value of the square root of ninety-seven rounded to the nearest thousandth?

• 9.850

• 9.849

• 9.848

• 9.847

Between which two integers does the square root of fifty-seven lie?

• 6 and 7

• 9 and 10

• 7 and 8

• 8 and 9

What is the approximate value of the square root of fifty-seven rounded to the nearest thousandth?

• 7.552

• 7.551

• 7.550

• 7.549