The video tutorial covers methods to compare rational and irrational numbers, focusing on exercises that involve calculating and comparing square roots and cube roots. It includes a series of exercises and challenge problems, encouraging students to use rational approximations and avoid over-reliance on calculators. The lesson concludes with a summary of the key concepts and methods used.

What is the main focus of the lesson on comparing numbers?

• Using only mental math for all problems

• Memorizing all square and cube roots

• Avoiding calculator shortcuts and using approximations

• Using calculators for all calculations

Which of the following is true about the cube root of 64?

• It is greater than 4.25

• It is equal to 4.25

• It is equal to 5

• It is less than 4.25

How can you express 319/45 as a decimal?

• 7.08 with 7 repeating

• 7.08 with 9 repeating

• 7.08 with 0 repeating

• 7.08 with 8 repeating

What is the square root of 121?

• 10

• 11

• 13

• 12

Which number is greater: the square root of 50 or 319/45?

• Square root of 50

• 319/45

• Cannot be determined

• They are equal

Where does the square root of 28 lie on the number line?

• Between 5.3 and 5.4

• Between 5.4 and 5.5

• Between 5.2 and 5.3

• Between 5.1 and 5.2

Which is larger: the square root of 5 or the cube root of 11?

• They are equal

• Cannot be determined

• Cube root of 11

• Square root of 5

What is the approximate length of one side of the chessboard if each square has an area of 3 square inches?

• 13.5 inches

• 14.0 inches

• 13.8 inches

• 14.2 inches

How many squares are there on the chessboard?

• 256

• 128

• 32

• 64

What is the square root of 3 rounded to the nearest hundredth?

• 1.72

• 1.73

• 1.74

• 1.75