4. What is the cube root of 5?

Ans. 1.726, nearly.

5. What is the cube root of?

Ans. 0.9353, nearly.

6. What is the cube root of ?

Ans. 0.8736, nearly.

7. What is the cube root of 47?

Ans. 3.6173, nearly.

8. What is the cube root of 1014?

Ans. 4.6592, nearly.

9. What is the cube root of 9?

Ans. 21085, nearly.

Case IV.

When there are many decimal places required in the root, we may, after obtaining one more decimal figure than half the required number, find the rest by dividing the remainder by the last term of the second column.

Before dividing, we can omit from the right of the divisor so many figures as to leave but one more than the number of additional figures required in the root, observing to omit from the right of the dividend one figure less than was omitted in the divisor. The division must then be performed according to the abridged method, as explained under Art. 41.

EXAMPLES.

1. What is the cube root of 7, carried to 9 decimal

places?

In this example, we proceed in the usual way, until we obtain 1.91293; the remainder is 12984369243; the last term of the second column is 109777313919; therefore, we obtain four more figures by dividing 12984369243 by 109777313919; but these four figures may be obtained with equal accuracy by dividing 12984 by 10977, which gives the remaining figures 1182.

2. Extract the cube root of =0.25 to 13 decimal places.

In this example, after obtaining seven decimal figures in the root, by the usual process, the remainder was 29701189129875, and the last term in the second column was 119054974974025; and, since we wish but six figures by division, we reject seven figures from the right of the remainder, and eight figures from the right of the term of the second column, and then divide by the rule

202

HIGHER ARITHMETIC.

for abridging the work, Art. 41, and obtain the remaining figures of the root.

3. Extract the cube root of 9 to 9 decimals

4. What is the cube root of 154 to 5 decimal places? Ans. 250222.

5. What is the cube root of 이니시에이비에에 to 8 decimals? Ans. 0.68278406. 6. What is the cube root of 0.0000031502374 to 13 decimals? Ans. 0.0146593403377. 7. What is the cube root of to 21 decimals?

Ans. 0.793700525984099737376.

8. What is the cube root of to 10 decimals?

Ans. 0.5227579585.

9. What is the cube root of to 7 decimals?

Ans. 0.9032157.

APPLICATION OF THE CUBE ROOT.

10. What is the cube root of 5 to 8 decimals? Ans. 013992727.

EXAMPLES

203

INVOLVING THE

PRINCIPLES OF THE CUBE ROOT.

79. It is an established theorem of geometry, that all similar solids are to each other as the cubes of their like dimensions.

1. If a cannon ball 3 inches in diameter weigh 8 pounds, what will a ball of the same metal weigh, whose diameter is 4 inches?

By the above theorem, we have 33:43:: 8 pounds : 18 pound, for the answer.

2. Suppose the diameter of the sun to be 887681 miles; the diameter of the earth, 7912 miles. How many times greater in bulk is the sun than the earth?

(887681)3=699472706450842241; (7912)3=495289174528;

699472706450842241 ÷ 495289174528 = 1412251

times, nearly.

3. How many cubic quarter inches can be made out of a cubic inch? Ans. 64.

4. Required the dimensions of a rectangular box,

which shall contain 20000 solid inches; the length, breadth, and depth being to each other as 4, 3, and 2.