MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

... find the approximate value of √5. In order to determine √5, let ...

5 ÷ G1 = 2.5

5 ÷ G2 = 2.222

5 ÷ G3 = 2.236

That means √5 is approximately 2.236.

5 ÷ G1 = 2.5

5 ÷ G2 = 2.222

5 ÷ G3 = 2.236

That means √5 is approximately 2.236.