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46656(36 Abs. 3a 30 Brosteet cube 27

3ta

90=30 times a.2790)19656

square of an 19656

300

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16200-300 times the są ofiaxe. 30 times the sq. of exas23240 cubie of e.

216 Liisi asal sirin

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subtrahend, 19666/*). DE
i ?): 2

6C

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365square of e.

6=0 il ,

2.16cube of e. 2. Required the cabe root of 153990656. Ans. 536. 3. What is the cube root of 47652901988,747336.

Ans. 3625,46. 4. Required the cube root of 68921. Ans. 4 ko.

5. Required the cube root of 262,144.

Ans. 6,4. 6. Required the cube root of 69426,531. Ans. 41,1. 7. Required the cube root of 3000729.

Ans.,09. 8. What is the cube root of,000000343 ? Ans. ,007.

A general rule for extracting the roots of all powers.

1. Prepare the given number for extraction, by pointing off from the unit place, as the root required directs,

2. Find the first figure in the root by your own judgment, or by inspection into the table of powers.

3. Subtract it from the given number.

4. Augment the remainder by the next figure in the given number, that is, by the first figure in the next point, and call this your dividend.

5. Involve the whole root last found, into the next inferior power to that which is given.

6. Multiply it by the index of the given power, and call this your divisor.

7. Find a quotient figure by common division, and annex it to the root.

8. Involve all the root, thus found, into the given power.

9. Subtract this power (always) from as many points of the given power as you have brought down, beginning at the lowest place.

10. To the remainder bring down the first figure of the next point for a new dividend.

11. Find a new divisor as before, and in like manner proceed till the work is ended.

EXAMPLES.

.:7.1. What is the cube root of 11550 1303? "***

* This must sometimes be taken less than the divisor would give, as is often the case in the square and cube roots, by the other method, so as to have the involved root, not exceed tho resolvend.

115501303( 487 Ansi
64

46,516 dividend

110592 subtrahend.

6912)49093 dividend.

115501303 subtrahend.

4X *8 divisor.

3 48 X 48X

subtrahend. 48 X 48X5331912-divisor.

487 X 487 X 487=115501303 subtrahend. 2. What is the biquadrate root of 56249134561 ?

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256)3064 dividend. 3.14 P

01).; 01.3456 5308416 subtrahend. ikinci

..4442368)3164974 dividend.

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56249134561 subtrahend.

4X

.: 4% 4* 4—256 divisor, 48 x 48 x 48 x 48–5308416 subtrahend. 48 x 48 x 48 x 45442368 divisor. 487 X 487 X 487 X 48756249134561 subtrahend.

* The most simple method of extracting the biquadrate root is to extract the square root of the given number, and then extract the square root of the square root thus found; this secpnd square root' will be the biquadrate root of the given tuinber.

MISCELLANEOUS QUESTIONS.

1

root?

de I demand the sum of 1738, added to itself. T!

Ans. 3476. 2. What is, the difference between 14676, and the fourth of itself?)

Ans. 11007. 3. Required the product of 865, multiplied by itself.

Ans. 133285. 4. Admit 476 be the square root of a number, what will be the quotient of that number, divided by half its

Ans. 952. 5. There is in three bags the sum of $1468, viz. in the first bag $461, in the second, $581 ; how much is in the third bag ?

Ans. $426. 6. What number is that which if multiplied by 17, the product will be 221 cm

Ans. 13. 7. A and Bowes several debts, the less debt being that of A, is $2173, the difference of the two is $371 ; what is B's debt?in

Ans. $2544. 8. A captain, and 160 sailors took a prize worth $4532, of which the captain had for his share, and the rest was equally divided among the sailors ; ; what was each man's part ?

The captain had $906,40. Ans.

each sailor, 22,66. 9. What number is that from which if you take-786, the remainder will be 340 ?

Ans. 1066. 10. Whạt number is that which being added to 706, their suin will be 1538/?sivo

Ans. 832, 11. What pumber is that which being divided by 72, the quotient will be 19 ?

Ans, 1 368. 12. If stock be bought when it is worth $650 per cent, and sold again when it is worth $130 per cent. how much is lost in buying and selling $400 capital stock ?

Ans. $2080. 13. A man at the age of 25 years had a son born, who lived 46 years, and then died ; after which time the father lived, 17 years abroa and 23 years at lyome, and then died ako ; what was the age of the father when he died ?

Ans. 111

years.

1

Ans. A, 626 13mm

Ind how much Ans. 8960.

14. Three men traded in £120 ; the sums they put in were

in sich they gained

proportion, that as often as A had £5 of the gain, B had £7, and as often as B had £4, C had £6; what was each man's share of the gain ?

B, 37 6 8

C, 5600 15. A, B and C, freight a ship with goods to the value $11088, of which A put in $1107, B $2691, by reason of a storm, one third of the goods were lost what was C's share of the first cost; and each man's share of the loss?

Ans. C's share of cost $7290,

A's $369 Shares of the loss. B's' 897

C's 2430 16. A and B traded in company, and gained 8100; A put in $640, B put in so much that he must receive $60 of the gain ; I demand how much B put in ?

Ans. $960. 17. What is the value of 27 dozen and 10 pounds of candles, at 5d. per Ib?

Ans. £6 19 2 18. Bought 28 quarters, and 2 bushels of wheat, at 4s. 6d. per bushel ; what is its whole value ?

Ans. £ $0 17. 19. How much can a man earn in 20 weeks, at 75 çents per day, Sundays excepted ? $Ans. 90.

20. A, B and C, traded together, A put in I know not how much, B put in 20 pieces of cloth, and C put in $500, and they gained $1000, whereof A ought to have $350, and B 8400 ; what was C's share of the gain, how much did A put in, and how much was B's cloth worth?

C's share of the gain was $250. Ans. A put in 8700.

B's cloth was worth $800. 21. A merchant bought six bags of hops, weighing as follows, viz. No. 1, 3cwt. Sqrs. 201b ; No. 2, 3cwt. 2qrs. 261b ;; No. 3, 3cwt. 241b; No. 4, 3cwt. 3qrs. No. 5, 2cwt. 2qrs. 221b"; No. 6, 2cwt. 2qrs. 261b ; besides 5 packets, three of which weighed 76_lb. each, and the other two 624lb. each ; what is the weight of the whole ?

Ans. 22cwt. Ogrs, 24lb.

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