Fast Way of Creating a P Chk

Now that you’d learned all the details in square edging a five or six digits perfect square number, it would be easier for you to understand this fast-track version of square edging.

Given problem

√ 62,001

Step 1:

Follow the instructions in 3D/4D.SE

√ 6’20’01

2 N 1

2 N 9

Take Note: As long as you become familiar with the rules in 5D/6D.SE, I will allow you not to include a zero before 6 in √ 06’20’01, as a strict rule in SSQ

Step 2:

Create a Parameter Checker

As a first rule, always write this phrase “ Let P = “ and then copy the first two groups of digits of the given problem, followed by two dots

Let P = 6’20..

Helpful Tips:

Fast Way of Creating a Parameter Checker

1) Check the first digit of any of the two possible square roots. Use it as the reference digit.

The first digits of the possible square roots (2N1and 2N9) are the same. They are all equal to 2.

reference digit = 2

2) Find a number, next to the reference digit, higher by 1. Put a zero after it together with the ‘two dots’ notation.

Next to 2 is 3. Writing 0 and .. , they will appear as this:

30..

3) On the next line, write down the reference digit and follow it with a digit ‘5’ and the ‘two dots’ notation.

30..

25..

4) On the third line, just copy the reference digit and follow it with a ‘0’ digit and the ‘two dots’ notation.

30..

25..

20..

5) Square them all. Include the ‘two dots’ notations at the end of each line.

30.. ² = 9’00..

25.. ² = 6’25..

20.. ² = 4’00..

Below will be the ‘general form’ that you must always follow in creating a P-Checker

P-Chk

Let P = 6’20..

30.. ² = 9’00..

25.. ² = 6’25..

20.. ² = 4’00..

Using the value of P, find out where it is located by looking at the right side values of the P-Chk.

If you will notice P = 6’20.. is above 4’00.. but below 6’25..

25.. ² = 6’25..

…………… } P = 6’20..

20.. ² = 4’00..

Determine if N is 5↑ or 4↓

Five Up and Four Down

25..² is also known as the middle-half square of 20..² and 30..². The 5 in 25..² actually represent the “next digit after the first digit”. We need to know if the next possible digit belongs to numbers from 5, 6, 7, 8 or 9 (five up) or belongs to 4, 3, 2, 1 or 0 (four down). So the Mid-half is also a reference, in knowing if the square root is in the HLA (higher limit area), or in LLA (Lower Limit Area).

…. 30.. ² = 9’00..

…{ Higher Limit Area

…. 25.. ² = 6’25..

4↓{ Lower Limit Area

…. 20.. ² = 4’00..

Write down below, “N = 4, 3, 2, 1, 0”

…. 30.. ² = 9’00..

…. 25.. ² = 6’25..

4↓{ …………… } P = 6’20..

…. 20.. ² = 4’00..

N = 4, 3, 2, 1, 0

Step 3:

Find out the Missing Digits

2N1² = ..nn’01 ← PSL

...Nx1x2 = ..0 ←SP1 (Add this SP1 to PSL)

....................01 ← T Sum

Nx2 = ..0

N = 0, 5

201

Take note: No need to write down 251 because the P-Chk gave as a hint that the true square root is at 4↓

2N9² = ..nn’81 ← PSL

...Nx9x2 = ..2 ←SP1 (Add SP1 toPSL)

....................01 ← TSum (provided that TSum aligned to PSL)

Nx18 = Nx8 = ..2

N = 4, 9

249

Take Note: With the use of parameter checker, we minimized at once the possible square roots from four into only two possible square roots.

Step 4:

To know it quickly which among the two possible square roots is the true square root, use the Square root locator. But this time, instead of writing down too many numbers, simply write down H, M and L and follow these mathematical operations;

1) Add H and L

2) Divide by 2. ( I represented it as _____/2 as to directly divide 10’25 by 2)

3) This is important. Always subtract the quotient by 6. It is much nearer to the “true square value” of the middle number of 20.. and 25.. ( which is 22.5..), than simply averaging the values of 6’25.. and 4’00..

H = 6’25..

M = ?

L = 4’00..

….10’25 / 2

….. 5’12 - 6

M = 5’06

1) Add H and L

2) Divide by 2. ( I represented it as _____/2) as to directly divide 10’25 by 2

3) This is important. Always subtract the quotient by 6. It is much nearer to the “true square value” of the middle number of 20.. and 25.. ( which is 22.5..), than simply averaging the values of 6’25.. and 4’00..

Our Square Root Locator will appear this way;

Sq. Rt. Loc

H = 6’25..

M = 5’06

L = 4’00..

4) Arrange the two possible square roots. On the left, is the lower square root with a down arrow (↓) and on the right, the higher square root with an up arrow (↑). Locate P (remember, P = 6’20..), by using the above Sq. Rt. Locator

↓201 ……………. 249↑

… H = 6’25..

↑ { ……….. } P = 6’20..

… M = 5’06

… L = 4’00..

The ‘up arrow’ shows that the true square root is in the upper portion of the HLA, so we choose 249 with an up arrow, as our answer.

√ 62,001 = 249