how to find square root of 3 to 4 digits
The only limitation of Square Edging is that it is only applicable in taking the square roots of numbers called perfect squares. The square roots of perfect squares are always in a “whole numbers”, never as fractions or decimal numbers. In fact, from 1 up to 100, there are only 10 perfect squares. While from 101 up to 10,000, there are only 90 perfect squares. The rest (9,900 other numbers) are useless in dealing with this format of S.E. But TRUST ME, it will WORTH A LOT.
I divided the topics into three;
1) 3D/4D.SE
2) 5D/6D.SE
3) 7D/8D.SE
Four Digit Square Edging (3D/4D.SE)
WARNING:
To easily understand this method of Square Edging, I highly recommend that you first study the SSQ Method.
Let us start by taking the square root of a four-digit number.
Given Problem: What is the square root of 2,304?
√2,304 = ?
Step 1
Count the digits of the given number. Re-group them by twos, starting from the last digit.
√23’04
Step 2
Find an index square, equal to or nearest to but less than the first group of digits of the given number. Write down the equivalent square root, below this first group of digits.
√23’04
4
Step 3:
Find a pair of index squares ending with the same last digit, as to the last digit of the given number. Write down below the last group of digits, their corresponding square roots.
04 is the last group of 23’04. The last digit of 04 is 4. There are two index squares that end with 4, these are 04and 64. Their equivalent square roots are, 2 and 8.
√23’04
4 2
_ 8
It would be helpful, if you memorized the pairs of index squares having the same last digits. I provided one for you.
Table of Complementary Index Squares
12 = 01
92 = 81
1 + 9 = 10
22 = 04
82 = 64
2 + 8 = 10
32 = 09
72 = 49
3 + 7 = 10
42 = 16
62 = 36
4 + 6 = 10
02 = 00
52 = 25
NO PAIRS
Step 4
Copy the first digit of the upper square root to complete the lower square root.
√23’04
4 2 ← first possible square root
4 8 ← second possible square root
Now, you determined the two possible square roots, only one of them is the ‘true’ square root of 2,304
Final Step
One way to find out which of the two is the true square root, apply the 2D.SSQ
... 422 = 16’04 ← PSL
+4x2x2 = 1'6 ← SP1 (provided that 6 of 16 aligned to 0 of PSL)
............. 17’64 ← T-Sum (provided that T-Sum aligned to PSL)
....482 = 16’64 ← PSL
+4x8x2 = 6'4 ← SP1 (provided that 4 of 64 aligned to the second 6 of PSL)
............ 23’04 ← T-Sum (provided that T-Sum aligned to PSL)
Comparing the results, the second equation matches the given number. We are now sure that 48 is the correct answer.
√2,304 = 48