Question

The ancient Babylonians developed a method for calculating nonperfect squares by 1700 BCE. Complete the statements to demonstrate how to use this method to find the approximate value of. In order to determine , let G1 = 2, a number whose square is close to 5. 5 ÷ G1 = , which is not equal to G1, so further action is necessary. Average 2 and G1 to find G2 = 2. 25. 5 ÷ G2 ≠(rounded to the nearest thousandth), which is not equal to G2, so further action is necessary. Average 2. 25 and G2 to find G3 = 2. 236. 5 ÷ G3 ≠(rounded to the nearest thousandth), which is equal to G3. That means is approximately 2. 236.

Answer 1

The steps taken to find the √5 using the ancient method is;

5/G1 = 2.5

5/G2 = 2.222

5/G3 = 2.236

We want to find √5 with the ancient Babylonian method for calculating non-perfect squares;

We are told that G1 = 2

Thus;

5/G1 = 2.5

We are told to average 2.25 and G2 to get 2.236

This means that;

(2.25 + G2)/2 = 2.236

2.25 + G2 = 2 × 2.236

G2 = 4.472 - 2.25

G2 = 2.222

Second step is;

5/G2 = 2.222

Finally;

5/G3 = 2.236

Read more about finding non-perfect squares at; brainly.com/question/9165533