Explanation:
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Square
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A square is a regular quadrilateral
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In geometry, a square is a regular quadrilateral. This means that
it has four equal sides and four equal angles (90-degree 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 r2 = 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 42 = 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 = 532. Use the
duplex method to find the square root of 2,809.
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Set down the number in groups
of two digits.
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Define a divisor,
a dividend and a quotient to find the root.
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Given 2809. Consider the first group, 28.
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Find the nearest perfect square below that group.
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The root of that perfect square is the first digit of our root.
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Since 28 > 25 and 25 = 52, take 5 as the first
digit in the square root.
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For the divisor take double this first digit (2 · 5),
which is 10.
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Next, set up a division framework with a colon.
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28: 0 9 is the dividend and 5: is the quotient.
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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.
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Calculate the remainder.
28: minus 25: is 3:.
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Append the remainder on the left of the next digit to get the
new dividend.
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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.)
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Repeat the operation.
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The zero remainder appended to 9. Nine is the next dividend.
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This provides a digit to the right of the colon so deduct the
duplex, 32 = 9.
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Subtracting this duplex from the dividend 9, a zero remainder
results.
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Ten into zero is zero. The next root digit is zero. The next
duplex is 2(3·0) = 0.
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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
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative
Commons Attribution- ShareAlike 3.0 Unported License.