July 16, 2024

# Square tricks

In this post, we will unveil a collection of square tricks that will make your calculations faster and more efficient. Whether you’re a student, a mathematician, or simply someone who loves number games, these techniques will surely amaze you. These simple techniques  can help you to find the square of a number  more quickly and easily.

Square tricks

Contents

# Square tricks numbers ending with ‘5 ‘

The first technique that we will discuss is how to instantly square numbers whose last digit is  5.  Remember , squaring is multiplying a number by itself.  The steps to follow are:

1. Take the number apart from 5.
2.  Multiply the number by the  number that comes after this number when counting.
3.  square the last digit (5×5)  and write 25 after it.

Example 1. Find the square of 85.

• In 85, the number apart from 5 is 8.
• The number that comes after 8 is 9.
• Multiply 8 x 9 =72.
• write 25 beside it.

Hence $\left&space;(&space;85&space;\right&space;)^{2}=85\times&space;85=$7225 .

Example 2.  Find the square of 205.

• In 205, the number apart from 5 is 20.
• The number that comes after 20 is 21.
• Multiply 20 x 21 =420.
• write 25 beside it.

Hence the square of 205 =42025 .

Example 3.  Find the square of  325.

• In 325, the number apart from 5 is 32.
• The number that comes after 32 is 33.
• Multiply 32 x 33 =1056.
• write 25 after it.

## Square tricks for  numbers between 50 and 60

The steps to find the square  of  numbers between  50 and 60 are below.

(i) Add 25 to the digit in the unit place  and put it as the left part of the answer .

(ii) Square the digit in the  in the unit place  and put it as the right part of the answer.(If it is a single digit , make it two digit number by adding ‘0’ before the number)

Example 1. Find the square of  58.

Sol. (i)  Add 25 to  unit place number(25+8=33) .  It is the left part of the answer.

(ii) Now find the square of unit digit 8 which is equal to 64.  Write it as the right part of the answer.

Hence the square of  58 is  33 64  .

Example 2. Find the square of 53.

Add  to 25 and get the left part of the answer as 28. Next,  we square 3 and get the answer 9 which we will put on the right side of the  answer.  However right side of the answer  should be a two-digit number. Hence we convert 9 as 09.

Thus the square of 53 is 2809.

### Square of numbers ending with digit 1

To get the square of any  such number, just write the square of previous number then add the previous number and the number whose square is being asked.

For example : $\left&space;(&space;31&space;\right&space;)^{2}=\left&space;(&space;30&space;\right&space;)^{2}&space;+(30+31)=961$

$\left&space;(&space;81&space;\right&space;)^{2}=\left&space;(&space;80&space;\right&space;)^{2}&space;+(80+81)=6561$

$\left&space;(&space;131&space;\right&space;)^{2}=\left&space;(1&space;30&space;\right&space;)^{2}&space;+(130+131)=16900+261=&space;17161$

#### Square of numbers ending with digit 9

To get the square of any  such number, just write the square of next number then subtract the addition of next number and the number whose square is being asked.

Example:(i)  $39^{2}=(40)^{2}-(39+40)=&space;1600-79=&space;1521$

(ii)  $249^{2}=(250)^{2}-(249+250)=62500-499=&space;62001$

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#### Bina singh

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