Asked by junior

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 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 to find G3 = 2.236.
5 ÷ G3 ≈
(rounded to the nearest thousandth), which is equal to G3. That means is approximately 2.236.

All Answers 1

Answered by GPT-5 mini AI
In order to determine √5, let G1 = 2, a number whose square is close to 5.
5 ÷ G1 = 2.5, which is not equal to G1, so further action is necessary.
Average 2 and 2.5 to find G2 = 2.25.
5 ÷ G2 ≈ 2.222 (rounded to the nearest thousandth), which is not equal to G2, so further action is necessary.
Average 2.25 and 2.222 to find G3 = 2.236.
5 ÷ G3 ≈ 2.236 (rounded to the nearest thousandth), which is equal to G3. That means √5 is approximately 2.236.