Again, a number is called the cube root of its cube. 73 = 343. Therefore, the cube root of 343 is 7.
The “cube root of 343” is written ∛343.
A perfect square is a number whose square root is a whole number. A perfect cube is a number whose cube root is a whole number.
Square Root.—If a number can be put into prime factors, its square root can be written down by inspection.
Example: Find the square root of 27225.
| Since 27225 | = | 32 | × | 52 | × | 112. | |
| ∴ √27225 | = | 3 | × | 5 | × | 11 | = 165 Ans. |
Rule for Digits.—We know that √1 = 1, and √100 = 10. Therefore, the square root of any number which lies between 1 and 100 lies between 1 and 10; i.e., if a number contains one or two digits, its square root consists of one digit.
Similarly, since √100 = 10 and √10000 = 100, the square root of a number between 100 and 10000 lies between 10 and 100. That is, if a number contains three or four digits, its square root consists of two digits.
Proceeding in this way, we obtain a general result—viz., the square of a number has either twice as many digits as the number, or one less than twice as many.
Hence, to ascertain the number of digits in the square root of a perfect square, mark off the [879] digits in pairs, beginning from the right. Each pair marked off gives a digit in the square root; and, if there is an odd digit remaining, that digit also gives a digit in the square root.