Approximating the Square Root of 45

The video tutorial demonstrates how to approximate the square root of 45 to the hundredths place without using a calculator. It begins by identifying the perfect squares around 45, establishing that the square root lies between 6 and 7. The instructor uses fractions to make an initial guess of 6.7, then refines this guess by calculating 6.7 squared. After further refinement, the instructor determines that 6.71 is a closer approximation to the square root of 45, as it results in a value slightly above 45 when squared.

What is the main goal of the problem discussed in the video?

• To approximate the square root of 45 to the hundredths place without a calculator.

• To compare the square roots of 36 and 49.

• To find the exact square root of 45 using a calculator.

• To determine if 45 is a perfect square.

Which two perfect squares are used to approximate the square root of 45?

• 36 and 49

• 16 and 25

• 49 and 64

• 25 and 36

What is the significance of the fraction 9/13 in the approximation process?

• It is used to calculate the exact square root of 45.

• It represents the distance from 36 to 45.

• It is the decimal approximation of the square root of 45.

• It shows how far 45 is from 36 in relation to the gap between 36 and 49.

What is the decimal approximation of 9/13?

• 0.75

• 0.69

• 0.85

• 0.57

Why is 6.7 chosen as an initial guess for the square root of 45?

• Because it is the average of 36 and 49.

• Because it is closer to 7 than to 6.

• Because it is exactly halfway between 6 and 7.

• Because it is a perfect square.

What is the result of squaring 6.7?

• 44.49

• 45.00

• 44.89

• 45.24

Why is 6.71 considered a better approximation than 6.7?

• Because 6.71 is easier to calculate.

• Because 6.71 is a perfect square.

• Because 6.71 squared is closer to 45 than 6.7 squared.

• Because 6.71 squared is exactly 45.

What is the result of squaring 6.71?

• 44.89

• 45.0241

• 45.00

• 44.49

How does the video suggest verifying the approximation of the square root of 45?

• By finding the average of 6.7 and 6.71.

• By comparing the squares of 6.7 and 6.71 to 45.

• By calculating the square root of 49.

• By using a calculator to check the result.

What is the final approximation of the square root of 45 to the hundredths place?

• 6.70

• 6.75

• 6.69

• 6.71