600 square of 5 x by triple of 8. 960 triple of 5 × by square of 8. 102125 subtrahend. 19714779 second resolvend. 255 triple of 85. 217005 second divisor. 729 cube of 9. 20655 square of 9 x by triple of 85. triple of 9 x by square of 85. 195075 19714779 second subtrahend. PROOF. Here 8.59 x 8.59 x 8.59 73.7881 × 8.59 = 633.839779, the same as the given number. 1200 square of 2 x by triple of 100. triple of 2 x by square of 100. 60000 6012008 subtrahend. PROOF. Here 10.02 x 10.02 x 10.02 100.4004 x 10.02 = 1006.012008, the same as the given number. gre square of 6 x by triple of 9. 1458 triple of 6 x by square of 9. 135736 subtrahend. 13890125 second resolvend. ess triple of 96. 27648 triple square of 96. 276768 second divisor. 125 cube of 5. 7900 square of 5 x by triple 96. 138240 triple of 5 × by square of 96. 18800125 second subtrahend. PROOF. Here 963 x 963 x 965 = .931225 x 965 = Sess2125, the same as the given number. 155736 subtrahend. 20025904 second resolvend. 288 triple of 96. 27648 triple square of 96. 276768 second divisor. 343 cube of 7. 14112 square of 7 x by triple of 96. 193536 triple of 7 x by square of 96. 19495063 second subtrahend. 530841 remainder. PROOF. Here .967 x .967 × .967 = .935089 x .967 = .904231063, the cube of the root; to which add the remainder, and we obtain .904761904, the proof required. CUBE ROOT, APPLIED TO THE Solution of several useful Mathematical Problems. PROBLEM I. To find the side of a cubical vessel that shall be equal in content to any given vessel, whose form is that of a parallelopipedon, a cylinder, a prism, a cone, &c. &c. EXAM. 1. 3 Here 216000 = 60 inches, the answer required. EXAM. 2. Here 231 x 43 9933, the number of cubic 3 inches in 43 wine gallons; and √9933 = 21.496 inches, the side required. EXAM. 3. Here 2150.42 × 48 103220.16, the number of cubic inches contained in 48 malt bushels; and ✔103220.16 46.908 inches, the answer required. |