Estimating and Comparing Square Roots

This video tutorial covers lesson 14.4 on approximating square roots. It is divided into three main parts: classifying numbers, estimating square roots, and comparing square roots. The lesson begins with an introduction to irrational numbers and their characteristics, followed by a diagram to help understand different types of numbers. The tutorial then moves on to estimating square roots by finding the closest decimal approximation. Finally, it discusses comparing square roots and ordering numbers based on their values.

Which of the following is an irrational number?

• π

• 0.5

• 4

• 2

What type of number is -3?

• Natural number

• Whole number

• Irrational number

• Integer

Why is the square root of 12 considered irrational?

• It is a perfect square

• It can be written as a fraction

• It does not repeat or terminate

• It is a whole number

Which of the following is a rational number?

• π

• Square root of 10

• 0.333...

• Square root of 2

What is the estimated value of the square root of 8 to the nearest tenth?

• 2.5

• 2.8

• 3.0

• 3.2

Between which two integers does the square root of 110 lie?

• 11 and 12

• 10 and 11

• 12 and 13

• 9 and 10

What is the estimated value of the square root of 33.3 to the nearest tenth?

• 6.0

• 6.2

• 5.5

• 5.8

Which of the following is greater: 4.2 or the square root of 23?

• 4.2

• Square root of 23

• Cannot be determined

• Both are equal

What is the approximate value of the square root of 10?

• 3.5

• 3.2

• 2.5

• 3.0

Which number is always greater: a positive number or a negative number?

• Both are equal

• Negative number

• Positive number

• Cannot be determined