## Err err err i s

For numbers from 25 to 50. First take the difference between the number and 25 for the hundreds and square the difference between the number and 50 for the tens and units. As for example, to square 39:—

The difference between 25 and 39 is 14. The number 14 gives the first two numbers of the answer.

The difference between 50 and 39 is 11. Which when squared gives 121:— To 121, we add fourteen hundred from the first step, and the answer 1521 equals 39 squared.

For numbers from 50 to 100. First take twice the difference between the number given and fifty for the hundreds and then square the difference between the given number and 100 for the tens and units.

(2) Extraction of Square Roots

The performer must first memorise the following table which shows the square of the digits one to nine:—

### Digit 123456789

Square 1 4 9 16 • 25 36 49 64 81 Suppose we are asked to extract the square root of the number 3136. First we consider only the two starting figures; the number nearest to 31 in the above table is 25—it must be more than 25 but not greater than 36. The table shows that 25 is represented by 5. Hence 5 will be the first figure of the square root of 3136. The last digit of this number is 6. There are two squares terminating with 6 in the above table and the number opposite them is one that will end the answer. However, we must be able to tell which of the sixes to use since one represents six and the other four. Take, the answer to the first step—which was 5, multiply this by itself giving 25, deduct this from the first two figures in the original number (31) and six remains. This figure six is larger than the one we have multiplied (5) so select from the above table the larger of the two numbers terminating with six. The figure opposite then gives the second number in the root; the root of 3136 is 56.

(3) Cubing

To find the cube of any two figure number, you must first know or work out the cube of the units one to nine. It will pay you to learn these because they can be used for other calculating effects shown later:— Digit 12345 6 7 8 9 Cube 1 8 27 64 125 216 343 512 729 Suppose now you are requested to find the cube of the number 62. Cube the first figure—6 and put it down in thousands, to the left of the cube of two. That is of six, 216, and of two, 8, which equals 216,008. To this add the product of:—

62 x 6 x 2 x 3. i.e. 62 x 36. equals 2232. Place this under the first number, moving the units figure one step to the left and add the two lines together.

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