Explanation:
Square

A square is a regular quadrilateral

In geometry, a square is a regular quadrilateral. This means that
it has four equal sides and four equal angles (90degree angles, or right angles). A square with vertices ABCD would be denoted ABCD.
The perimeter of a square whose
sides have length t is
and the area is
(Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Square_(geometry)
In mathematics, a square root of a number x is a number r such that r^{2} = x, or, in other words, a
number r whose square (the result of multiplying
the number by itself, or r × r) is x. For example, 4 is a square
root of 16 because 4^{2} = 16. (Our solved example in mathguru.com uses this concept)
http://en.wikipedia.org/wiki/Square_root
Example 1, by discussion
Consider the perfect square 2809 = 53^{2}. Use the
duplex method to find the square root of 2,809.
1.
Set down the number in groups
of two digits.
2.
Define a divisor,
a dividend and a quotient to find the root.
3.
Given 2809. Consider the first group, 28.
4.
Find the nearest perfect square below that group.
5.
The root of that perfect square is the first digit of our root.
6.
Since 28 > 25 and 25 = 5^{2}, take 5 as the first
digit in the square root.
7.
For the divisor take double this first digit (2 · 5),
which is 10.
8.
Next, set up a division framework with a colon.
9.
28: 0 9 is the dividend and 5: is the quotient.
10.
Put a colon to the right of 28 and 5 and keep the colons lined
up vertically. The duplex is calculated only on quotient digits
to the right of the colon.
11.
Calculate the remainder.
28: minus 25: is 3:.
12.
Append the remainder on the left of the next digit to get the
new dividend.
13.
Here, append 3 to the next dividend digit 0, which makes the new
dividend 30. The divisor 10 goes into 30 just 3 times. (No reserve needed here
for subsequent deductions.)
14.
Repeat the operation.
15.
The zero remainder appended to 9. Nine is the next dividend.
16.
This provides a digit to the right of the colon so deduct the
duplex, 3^{2} = 9.
17.
Subtracting this duplex from the dividend 9, a zero remainder
results.
18.
Ten into zero is zero. The next root digit is zero. The next
duplex is 2(3·0) = 0.
19.
The dividend is zero. This is an exact square root, 53. (Our
solved example in mathguru.com uses this concept)
http://en.wikipedia.org/wiki/Methods_of_computing_square_roots
The above explanation is copied from
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Commons Attribution ShareAlike 3.0 Unported License.