The radical sign with a figure 3 over it (∛ ) means that the cube root of the number following it is to be taken.
∛125 reads, “The cube root of 125.”
If we can find the prime factors of any perfect cube, we can write down its cube root by inspection.
Example: Find the cube root of 74088.
| 8 | 74088 |
| 9 | 9261 |
| 3 | 1029 |
| 7 | 343 |
| 7 | 49 |
| 7 |
| ∴ | 74088 | = | 8 × 9 × 3 × 7 × 7 × 7 |
| = | 23 × 33 × 73 | ||
| ∴ | ∛74088 | = | 2 × 3 × 7 |
| = | 42 Ans. | ||
Rule for Digits.—Since 13 = 1 and 103 = 1000, therefore the cube of a number which lies between 1 and 10 lies between 1 and 1000, i. e., the cube of a number of one digit contains either one, two or three digits.
Again, since 103 = 1000 and 1003 = 1000000, the cube of a number of two digits contains either four, five, or six digits.
Proceeding in this way, we see that the cube of a number contains three times, or one less or two less than three times, as many digits as the number.
Hence, to find the number of digits in the cube root of a given number, we mark off the digits in sets of three, beginning at the decimal point, and marking both to the right and to the left.