Estimating the Square Root of 22

The video tutorial demonstrates how to estimate the square root of 22 using trial and error. It begins by identifying the perfect squares between which 22 lies, then makes an initial approximation to the tenths place. The tutorial refines this approximation to the hundredths place, ultimately determining that 4.69 is the best estimate for the square root of 22. The process involves squaring the approximations and comparing them to 22 to find the closest value.

Which two perfect squares is 22 between?

• 9 and 16

• 16 and 25

• 25 and 36

• 4 and 9

What is the square root of 16?

• 3

• 4

• 5

• 6

Why is 4.7 chosen as the first approximation for the square root of 22?

• Because 22 is closer to 16

• Because 22 is closer to 25

• Because 4.7 is a perfect square

• Because 4.7 is less than 4.6

What is the result of squaring 4.7?

• 23.04

• 24.01

• 22.09

• 21.16

Why is 4.69 chosen for the two decimal place approximation?

• Because 4.69 is closer to 5

• Because 4.69 is a perfect square

• Because 4.69 squared is less than 22

• Because 4.69 squared is more than 22

What is the result of squaring 4.69?

• 21.9961

• 22.16

• 22.09

• 21.9024

Why is there no need to try 4.68 for the approximation?

• Because 4.68 is closer to 5

• Because 4.68 is a perfect square

• Because 4.68 squared is less than 21.9961

• Because 4.68 squared is more than 22

What is the final approximation of the square root of 22 to two decimal places?

• 4.70

• 4.71

• 4.69

• 4.68

What is the significance of the value 21.9961 in the approximation process?

• It is the result of squaring 4.6

• It is the result of squaring 4.7

• It is the result of squaring 4.69

• It is the result of squaring 4.68

What is the main goal of the estimation process described in the video?

• To determine if 22 is a perfect square

• To find the square root of 25

• To estimate the square root of 22 to the nearest hundredth

• To find the exact square root of 22