Perfect Squares Chart

Perfect squares chart :

 Perfect squares are defined as expressions or numbers that can be factored into two equal expressions or numbers.

For example,

x² + 2xy + y² = ( x + y) * ( x + y) , so  (x² + 2xy +  y²) is a perfect square of (x + y)

4 = 2*2 , so 4 is a perfect square of 2.

Algebra is widely used in day to day activities watch out for my forthcoming posts on translate to an algebraic expression and write an algebraic expression. I am sure they will be helpful.

Properties of Perfect Squares Chart

All perfect squares are non-negative ( at least in the real numbers' set).

• Square of 0 is 0.
• Squares of perfect numbers are the same as the squares of their positive counterparts,  

 For example           -1*-1 = 1*1 = 1,  (-2)²= 2²= 4

Difference between two perfect squares

Difference between a perfect square and the next perfect square is given by :

Square of a number n = n²

The next perfect square is square of the next number, that is, square of n + 1, so ( n + 1) ² = n² + 2n + 1

Difference between the two numbers =  2n + 1

So, if n² is a perfect square, the next perfect square will be n² + ( 2n + 1).

Example : 

100 = 10² is a perfect square.

Here, n = 10

So, the next perfect square will be 100+ 2*10 + 1 = 121 = 11²

Uses of Perfect Squares Chart

Included below is a chart of perfect squares of numbers from 1 to 25

Number n	Number Square n2
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64
9	81
10	100
11	121
12	144
13	169
14	196
15	225
16	256
17	289
18	324
19	361
20	400
21	441
22	484
23	529
24	576
25	625

Remember: 

• A square number can only end with digits 00,1,4,6,9, or 25
• Squares of even numbers are even, since (2n)² = 4n².
• Squares of odd numbers are odd, since (2n + 1)² = 4(n² + n) + 1.
• It follows that square roots of even square numbers are even, and square roots of odd square numbers are odd.

Uses of Perfect Squares :

Squaring is used in statistics in determining the standard deviation of a set of values. The deviation of each value  from the mean  of the set is defined as the difference . These deviations are squared, then a mean is taken of the new set of numbers (each of which is positive). This mean is the variance and its square root is the standard deviation. In finance, the volatility of a financial instrument is the standard deviation of its values.