# Extraction of the cubic root

**Extracting of the cubic root** - it's easy! If you tell a friend that you can count in your mind no worse than electronic computer, he, of course, will ridicule you. Then, without embarrassment, ask him to erect in a cube a number not more than a hundred. When he tells you the result, for example, the number 658503, you, to his amazement, almost without hesitation, call the number 87. The cube root of the six-figure number you extracted in the mind for a second!

How is this done?

First of all, you must firmly know a number of cubes of numbers:

1^{3}=1, 2^{3}=8, 3^{3}=27, 4^{3}=64, 5^{3}=125, 6^{3}=216, 7^{3}=343, 8^{3}=512, 9^{3}=729, 10^{3}=1000.

The extraction of the cubic root is done as follows:

From the named number, mentally separate three signs on the right from the comma (658,503). If the number that appears to the left of the comma is no more than three characters, the number erected in the cube was a two-digit number. The last figure of this number you call without hesitation - 7. After all, only 7 gives in the ending 3.

The first digit of the cube root is determined by the number to the left of the comma (658). What number, raised to the cube, will give 658? 9^{3} = 729, 8^{3} = 512.

We take a smaller number - this will be 8. So, the first digit of the cube root is 8, the second is 7. The number is 87.

After a little workout, extracting the cubic root is easily done in the mind.

With a constant density of matter, the dimensions of two similar bodies refer to each other as the cubic roots of their masses. So, if one watermelon weighs twice as much as another, its diameter, as well as the circumference, will be just slightly more than a quarter (26%) more than the first; and by eye it will seem that the difference in weight is not so significant. Therefore, in the absence of weights (sale by eye), it is usually more profitable to buy a larger fruit.

Interestingly, the extraction of the cube root can not be done with the compass and ruler. That is why the classical problems reducible to the extraction of the cubic root are insoluble: doubling the cube, trisection of the angle, and also constructing the regular heptagon.