EXAMPLE.

To extract the 5th root of 21035'8.

"

Here it appears that the 5th root is between 7.3 and 7·4. Taking 7.3, its 5th power is 20730-71593. Hence we have P = 21035'8, n = 5, r = 7•3 and A= 20730-71593; then

n + 1. A + n- · 1. †P : PC2 A :: r: Ror,

that is,

3 × 20780-71593 +2 × 21035·8 : 305·084 :: 73 :

1. What is the 3d root of 2? 2. What is the 3d root of 3214? 3. What is the 4th root of 2 ? 4. What is the 4th root of 97.41 ? 5. What is the 5th root of 2? 6. What is the 6th root of 21035.8? 7. What is the 6th root of 2? 8. What is the 7th root of 21035·8 ? 9. What is the 7th root of 2 ? 10. What is the 8th root of 21035'8 ? 11. What is the 8th root of 2? 12. What is the 9th root of 21035.8? 13. What is the 9th root of 2?

Ans. 1.259921.

Ans. 14.75758.

Ans. 1.189207.

Ans. 3.1415999.

Ans. 1.148699.

Ans. 5.254037.

Ans. 1.122462.
Ans. 4145392.
Ans. 1104089.
Ans. 3.470323.

Ans. 1.090508.

Ans. 3.022239.

Ans. 1.080059.

The following is a Table of squares and cubes, as also the square roots and cube roots, of all numbers from 1 to 1000, which will be found very useful on many occasions, in numeral calculations, when roots or powers are concerned.

A TABLE

90 A TABLE OF SQUARES, CUBES, AND ROOTS.