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.