In this post, we will discuss some useful maths shortcuts, Most of the students have quite a good sense of the squares of the first 15 integers are. You might get confused when it comes to 13’, 12’, 14’. Have a look on the following square of integers.

12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225

Here we have some more squares that the students must know:

162 = 256
202= 400
252 = 625
302 = 900

If you remember all these squares, its pretty good for your competitive Mathematics examination.

Well, if you are familiar with all these squares then you must be able to solve some complex equations.

For example

11 x 13, 14 x 16, 15×17 or 29×31.

At first look you might see it as a difficult equation but you can surely solve it in few seconds if you know the following smart shortcut.

Remember the basic algebra formula:

n2-1=(n-1)(n+1)

Suppose n=2

By knowing that 202=400, the product of one of the integer will be less than 20-the number 19 and the other one integer greater than 20-the number 21 will be 400-1 which is equal to 399.

Now try it with one of the numbers above.

For Example

122=144

Therefore,

11 x 13=143

For

29×31 =302-1 = 899

In this way, you will be operating difficult equations in a short while.