Point off the numbers into periods of three figures each, beginning at units. The greatest

number whose cube is contained in 45 is 3, which is the first figure of the root. Cube 3; subtract the result from 45, and annex 118 to the remainder, making the dividend 18,118. Take 3 times the square of 3, or 27, for a trial

divisor. Divide 18,118, exclusive of the two right-hand figures, by 27, making allowance for corrections to be added, for the next figure of the root, which is found to be 5. Take 3 times 3 times 5 for the first correction, and set it one place to the right of the trial divisor. Take the square of 5 for the second correction, and set it one figure to the right of the first correction. The sum of the trial divisor and the two corrections, 3175, is the complete divisor. Multiply 3175 by 5, the last figure of the root found, subtract the product 15,875 from 18,118, and annex 016 to the remainder, making the dividend 2,243,016. Take 3 times the square of 35 for the trial divisor. Find as before the next figure of the root 6, the first correction 630, the second correction 36, the complete divisor 373,836, the product 2,243,016, and the remainder 0. The cube root is 356. 2. Extract the cube root of 25, correct to the nearest hundredth. 25./000/000 [2.924

Extract the cube root, correct to the nearest hundredth, of:

SUGGESTION. Since 2 × 3 × 3 = 27, the cube root of 34 = 4.

NOTE. If a fraction in its lowest terms is a perfect cube, its terms are perfect cubes. If the terms of a fraction in its lowest terms are not perfect cubes, it is best to reduce the fraction to a decimal before extracting the cube root.

I. A traveler starts at longitude 75° 15′ W. and travels until his watch is 6 hours too slow.

What is then his longitude?

2. Sea water weighs 1026 grams per liter. How many metric tons of sea water will a tank hold if it is 2 meters long, 1 meter 5 decimeters wide, and 2 meters deep?

3.

The longitude of A is 2° E. When the time at A is 2 P.M., the time at B is 9.12 A.M. Find B's longitude.

4. One cubic centimeter of olive oil weighs 915 milligrams. Find the weight in grams of 15 liters 4 deciliters of olive oil.

5. If a kilogram of a certain substance is found to contain 2 grams 150 milligrams of adulterant, what is the per cent of adulterant in the substance?

6. If a traveler left San Francisco at noon Monday, Pacific time, and arrived at New York at noon Saturday, Eastern time, how long did it require him to make the journey?

7.

In how many days of 10 hours each will 25 men husk 5000 shocks of corn, if 2 men in 8 days of 12 hours each husk 640 shocks?

8. Extract the square root of 2, correct to the nearest ten-thousandth.

9. Extract the cube root of 2, correct to the nearest thousandth.

10. Air weighs about 1.29 grams per liter. Find the weight in kilograms of the air in a room 10 meters long, 8 meters wide, 2.5 meters high.

II. Find the cost of a bill of exchange on London for £15 6s. at 4.8775.

12. The longitude of A is 60° W. When the time at A is 9 A.M., the time at B is 4.12 P.M. Find B's longitude.

13. Two spheres of the same material weigh 216 lb. and 8 lb., respectively. If the diameter of the first is 1 ft., what is the diameter of the second?

14. What is the value of a quarter-quarter-section of land at $40 per acre?

15. If 360 cart loads of earth were removed in excavating a cellar 36 ft. long, 30 ft. wide, and 9 ft. deep, how many cart loads would have to be removed in excavating 3000 ft. of canal 60 ft. wide and 10 ft. deep?

16. Find the amount of square-edged inch boards that can be sawed from a log 32 in. in diameter and 30 ft. long.

17. Find the diagonal of a cube whose edge is 6 in. Answer correct to the nearest .01 in.

18. If a hectoliter of soft anthracite coal weighs 145 kilograms, what sum will be obtained by selling 200 cubic meters of this coal at $5 a metric ton?

19. If a cylindrical vessel 18 in. in diameter and 8 in. deep holds a bushel, what must be the dimensions of a vessel of the same shape to hold a peck?