MSM -3 is the simplest and direct method of extracting the square root of any number, big or small, perfect or non-perfect.

**√20**

1) Like in any rule, look for a square, equal or nearest the given number. Write down its square root value

__.... 4.__

**√20.00**

^{2} = 25.00

**4. 9^{2} = ?**

**4. 8^{2} = ?**

**4. 7^{2} = ?**

**4. 6^{2} = ?**

**4. 5^{2} = ? **

**4. 4^{2} = ? **

**4. 3^{2} = ?**

**4. 2^{2} = ?**

**4. 1^{2} = ?**

**4. 0^{2} = 16.00**

By using the technique we learned involving the “squares of five” (See: __SQUARES ENDING IN 5__ http://easysqrtsforkids.blogspot.com/2010/08/five-digitsix-digit-square-edging.html );

**4.5 ^{2} = 20.25**

**5.0 ^{2} = 25.00**

**4. 9^{2} = ?**

**4. 8^{2} = ?**

**4. 7^{2} = ?**

**4. 6^{2} = ?**

**4. 5^{2} = 20.25**

**4. 4^{2} = ? **

**4. 3^{2} = ?**

**4. 2^{2} = ?**

**4. 1^{2} = ?**

**4. 0^{2} = 16.00**

If you will notice, 20.25 is greater than 20. It follows then, that 20 is within the area of below 4.5

^{2}, (that is, within the range of 4.4

^{2}and 4.1

^{2}).

3) To avoid squaring individually, the numbers from 4.1 up to 4.4, we use the digit locator.

__5__^{2} = 20.25

__4.0 ^{2} = 16.00__

…….. **36.25**

**36.25 ÷ 2 = 18.12**

**18'12 – 6 = 18'06
**

**
**

**4. 5^{2} = 20.25**

**4. 4^{2} = ? **

**4. 3^{2} = ?**

**4. 25^{2} = 18.06**

**4. 2^{2} = ?**

**4. 1^{2} = ?**

**4. 0^{2} = 16.00**

You will notice that 20 is in-between 20.25 and 18.06, so we miniminized our choice of digits from 9 into only two – 4 and 3.

**4.4 ^{2} = 16.16**

__4x8 = ...3 2 .__

.......... **19.36** **≤ 20**

**4.3 ^{2} = 16.09**

__4x6 = ...2 4 .__

.......... **18.49** **≤ 20**

**19.36** and **18.49** are near to **20**, but the **nearest is 19.36**, so we choose **4** as our next digit.

**4.4 ^{2} = 19.36**

**4.4**, repeat the process by knowing the middle square value (**4.45 ^{2}**)

**4.4_ ^{2} = ?**

__IMPOTANT TIP __

**Knowing the **

**4.4 5^{2} = ?**

**25** next to the square value of already known digits

**19.36’25**

2) Simply copy the already known digits (44) and add to that ‘modified’ square value but make sure that the last digit of the known digits (44), is align to the third digit, from the last digit of the modified square value. (the modified square value is 19.36'25)

**4.5 ^{2} = 19.36’25**

__+ ‘’ = ____..... 44 .... __

.......... **19.80’25**

**4.475 ^{2}** and

**4.4725**

^{2}

__5__^{2} = 19.98’09’25

__‘’x10 = ____........ 4’47 ....__ (Ignore the decimal point)

.............. **20.02’56’25** **↓ **(the down arrow shows that P: 20 is in lower area)**
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**

**
**

**4.472 5^{2} = 19.99’87’84’25**

.................__......... 44’72 ...__

................ **20.00’32’56’25 ↓**

I believe that one’s you master this technique, extracting the square roots of numbers will be much easier to explain to any one, including grade school children.

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