Solution:
| 4·53·69 | ) | 213 | |
| 4 | |||
| 41 | 53 | ||
| 41 | |||
| 423 | 1269 | ||
| 1269 | |||
(1) Point off the number into periods of two figures each, as before.
(2) The square root of the first period is 2. 2 × 2 = 4. Write the 2 in the root and subtract the 4 from 4. Bring down the next period, 53.
(3) 2 × 2 = 4. (Remember the 4 is to be used as a trial divisor, being 2 × the tens.)
4 is contained in 5 about 1 time. Place 1 in the root, also on the right of the 4 in the divisor. Multiply 41 by 1. Subtract and bring down the next period.
(4) 2 × 21 = 42. 42 is the trial divisor. 126 ÷ 42 = about 3 times. Place the 3 in the root also at the right of the 42 in the divisor. Multiply out.
Square root = 213.
Cube Root.—The cube root of a number is one of the three equal factors of that number.
Thus, 5 is the cube root of 125, because 5 × 5 × 5 = 125.