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Example:Find Square Root using Long Division

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Square (geometry)


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 (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)




Square root


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)




Example 1, by discussion

Consider the perfect square 2809 = 532. 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 = 52, 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, 32 = 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)




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.