Square Root Approximation Techniques

The video tutorial demonstrates how to estimate the square root of 78 without using a calculator. It begins by identifying the perfect squares between which 78 lies, specifically 64 and 81. Since 78 is closer to 81, the square root of 81, which is 9, is used as a starting point for approximation. The tutorial then explains how to adjust this approximation by calculating a fraction, resulting in an estimated square root of approximately 8.83. This estimation is compared to the calculator's result, showing a close match.

Which two perfect squares is the number 78 between?

• 81 and 100

• 36 and 49

• 64 and 81

• 49 and 64

What is the square root of 81 used for in the approximation process?

• To serve as a reference point for approximation

• To determine the square root of 100

• To find the exact value of the square root of 78

• To calculate the square root of 64

Why is the fraction in the approximation process negative?

• Because the value must be greater than 9

• Because the value must be less than 9

• Because 78 is less than 81

• Because 78 is more than 64

What is the approximate value of the square root of 78 obtained through this method?

• 8.5

• 9.1

• 8.83

• 8.9

How does the approximation of the square root of 78 compare to the calculator's result?

• It is significantly higher

• It is a very close approximation

• It is significantly lower

• It is exactly the same