Fast cube root extraction. Effective trick and its solution

EFFECTIVE FOCUSES AND THEIR CLUES
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Fast cube root extraction. Focus Secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

A demonstration of the cube root trick begins by asking someone present to take any number from 1 to 100, cube it, and report the result aloud. After that, the demonstrator instantly calls the cube root of the named number.

Focus secret:

In order to show this trick, you must first learn the cubes of numbers from 1 to 10:

1 - 1

2 - 8

3 - 27

4 - 64

5 - 125

6 - 216

7 - 343

8 - 512

9 - 729

10 - 1000

When studying this table, it turns out that all the numbers that cubes end in are different, and in all cases, with the exception of 2 and 3, as well as 7 and 8, the last digit of the cube coincides with the number being cubed. In exceptional cases, the last digit of the cube is equal to the difference between 10 and the number being cubed.

Let us show how this circumstance is used to quickly extract the cube root. Let the viewer, raising a certain number into a cube, get, for example, 250047. The last digit of this number is 7, from which it immediately follows that the last digit of the cube root should be 3. The first digit of the cube root is found as follows. Let's cross out the last three digits of the cube (regardless of the number of its digits) and consider the numbers in front - in our case it is 250. The number 250 is located in the table of cubes between the six and seven cubes. The smaller of these numbers - in our case 6 - will be the first digit of the cube root. So the correct answer is 63.

To better understand the essence of the matter, we will give another example. Let the number 19683 be named. Its last digit 3 indicates that the last digit of the cube root will be 7. Crossing out the last three digits, we get the number 19, which lies between the cube of two and the cube of three. The smallest of these numbers will be 2, so the cube root we are looking for is 27. It may seem strange, but there are simpler rules for extracting integer roots from powers higher than the third. It is especially easy to find fifth roots, because any number and its fifth power always end in the same digit.

Author: M.Gardner

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