Variation of SE Telegram

Given Problem:

√97,574,884

Left Column

√97’57’48’84

... 9 ............ 2

... 9 ............ 8

Right Column

.P : 97’57

95 : 90’25↑

M : 5↑ ... /9750/

Left Column, 2nd Row

. N2 : 04

Nx4 : 8 . ... 2, 7

......... 8

.. 22 : 04’04

.2x4 : 00’8

........... 4’84

.Mx4 : 4 . 1, 6

........... 8

9622 (A)

.. 72 : 49’04

.7x4 : 02’8

........... 1’84

.Mx4 : 7 . (odd product)

........... 8 ≠ √P

Right Column, 2nd Row

... N8 : 64

. Nx6 : 2 . .... 2, 7

........... 8

28: ≠ √P

... 78 : 49’64

7x16 : 11’2 .

............ 0’84

. Mx6 : 8 . .... 3, 8

............ 8

9878 (B)

Left Column, 5^th Row

.. 100’ .. \

... 95’06/ ↑

... 90’25

. 190’25 / 2

... 95’12

Right Column, 5^th Row

√97,574,884 = 9,878

In the above example, there are two possible square roots that ‘automatically eliminated’ due to the reason that the sub-products tend to end in odd digit, which violate the general rule of SSQ that all sub-products must be in even numbers.

Take note that there is always a pattern when a “not a square root of P” notation appears on the left column or right column.

If it is in left column3^rd row, the next ≠ √P is on the right column, 2^nd row or vice versa.

If it is in the left column 2^nd row, the next ≠ √P is on the right column, 3^rd row and vice versa.

The notations /_750/ at 5↑ and /_250/ at 4↓ (in P Chk), are only reminders that in arranging the possible square roots, make sure that there should be two values less than the indicated notation and two other possible square roots greater than it, or else, there could be an error in the process.

FINAL WORDS:

I believe that some people would agree with me that this kind of technique in taking the square root of numbers is much easier. But I don’t intend to replace the traditional method of taking the square root of numbers (long hand division).

I have good reasons why this method will benefit grade school children

1) It will sharpen their skills in adding and multiplying numbers.

2) There is little division and subtraction. I do believe that children hate to divide or subtract large numbers.

3) It will introduce them to the idea of what squares and square roots of numbers are, which they will learn soon in trigonometry (Pythagoreans Theorem), and higher mathematics.

4) The introduction of letters (M, N, P etc), might be strange to them but at that early age, SE prepares them in some basic ideas of algebra. It is up to the parents or teachers’ imaginations. It could be this way “imagine M as a box, where we don’t know what digit is inside that box. “

5) It gives them ideas of the relationships of numbers, such as, which numbers have the same last digits or what number should be multiplied by such number to get a product ending with this and that.

6) SE is Three-in-One (like a 3-1 coffee?). They will learn to know the basic squares of numbers and at the same time, sharpen their skills in addition and multiplication (repeated addition and multiplication of numbers), all in a one package.

7) It is more like a guessing game, a fun way of doing arithmetic. Knowing the missing digits challenges them to work it out than giving them a task of multiplying two numbers or adding four-digit numbers where they don’t have a clue, what the answers should look like.

I am advocating this method, to become part of the curriculum in elementary schools. I am looking for people who would agree with me with this idea and help me spread this message.

As a TOKEN OF APPRECIATION, I wish people will call this method, Square Edging MSM-1 (as part of my name is included in it).

Why MSM-1? The reason is that there are two other methods:

MSM- 2 Square Edging Numbers ending in 25, where MSM-1 failed

MSM-3 Universal Square Edging, a true way of taking the square root of any number, perfect square or not that is much easier to use than the long-hand division method.

Fidel Mendoza Jr. (Author of MSM-1)