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.

Consider the following geometry problems in 3-space enter t or f depending on whether the statement is true or false. (you must enter t or f -- true and false will not work.) f equation editorequation editor 1. a plane and a line either intersect or are parallel t equation editorequation editor 2. two planes parallel to a third plane are parallel f equation editorequation editor 3. two lines either intersect or are parallel f equation editorequation editor 4. two planes orthogonal to a third plane are parallel f equation editorequation editor 5. two planes orthogonal to a line are parallel f equation editorequation editor 6. two planes either intersect or are parallel f equation editorequation editor 7. two lines orthogonal to a third line are parallel t equation editorequation editor 8. two lines parallel to a third line are parallel t equation editorequation editor 9. two planes parallel to a line are parallel f equation editorequation editor 10. two lines parallel to a plane are parallel f equation editorequation editor 11. two lines orthogonal to a plane are parallel