# Squares Tricks

Here are some of the Squares Tricks which you might find useful next time you go for an exam.

### Shortcut tricks to find square of  numbers which is nearer to 10x

Trick is X2 = (X+Y)(X-Y) + Y2
Here X is the actual number whose square we want to calculate.

To apply this trick we have to find out the value of ‘Y’. Let’s understand with the help of examples.

• Calculate square of 98
Let’s apply the above trick. We know that by adding 2 in 98, we get 100. Therefore value of Y is 2.
Thus,
982 = (98+2)(98-2) + 22 = 100 x 96 + 4 = 9604
• Calculate square of 103
Let’s apply the above trick. We know that by subtracting 3 from 103, we get 100. Therefore value of Y is 3.
Thus,
1032=(103-3)(103+3)+32=10600+9=10609

### Tricks to find out the value of a perfect square

This is a four step trick. Let’s understand it with the help of an example.

### Trick to find square of numbers between 40 and 50

Let’s understand this trick with the help of examples below:

• Calculate square of 46
• Step 1: Subtract 46 from 50 i.e. 50-46 = 4
• Step 2: Now subtract result of step 1 from 25 i.e. 25-4 = 21
21 will be the first two digits of our answer.
• Step 3: Now square the number obtained in step 1 i.e.
42 = 16 (This will be last two digits of our answer)
Therefore, answer is 462 = 2116.

### Trick to find square of numbers between 51 and 59

There are two methods to calculate the square of numbers between 51 and 59. Let’s apply these methods to calculate the square of 57.

• Method 1:
• Step 1: Subtract 50 from 57 i.e. 57-50 = 7
• Step 2: Now add result of step 1 to 25 i.e. 25+7 = 32
32 will be the first two digits of our answer.
• Step 3: Now square the number obtained in step 1 i.e.
72 = 49 (This will be last two digits of our answer)Therefore, answer is 572 = 3249.
• Method 2:
Here trick is 5A2=25+A/A2