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Bharthi Krishna Tritha, an Indian monk, wrote the book "VEDIC MATHEMATICS", which has a list of mathematical tricks to solve maths calculations faster than traditional methods. It gives the easiest way to solve addition, subtraction, multiplication, division, and related problems. Vedic mathematics can applied to pneumatics, statics, astronomy, and the financial domain.
Squaring Tricks! Square numbers faster

A number, when multiplied by the number itself the product obtained, is called "SQUARE OF THAT NUMBER ". Here are some examples followed by Square tricks.

Example
Number Square of the number
6^2 6 × 6 = 36
8^2 8 × 8 = 64
12^2 12 × 12 = 144

Type 1: Squaring of number ending with 5.

Sutra is "BY ONE MORE THAN PREVIOUS ONE"

Step 1: Add 1 to the first digit from the left and multiply by the number itself.
Step 2: Add 52 (25) at the end to the number obtained from step 1.
Number Steps
65
6 × (6 + 1)
= 6 × 7
= 42 Add 1 to the left number (6) and multiply by the number itself and

=4225 Add 52 (25) at the last of 42
Answer : 652 = 65 × 65 = 4225


Type 2: Squaring of numbers less than 50 and numbers not ending with 5.
Number Steps
34 50 - 16 = 34
52 = 25
= 25 + (-16)
= 9 Square the first digit (5) of first part (50) then add part (-16)
162 = 256 Square the second part of number (16)
9 + 256 = 1156 Add the answers got in step 1 (9)and step 2 (256)
Answer : 342 = 34 × 34 = 1156

Type 3: Squaring of numbers less than 50 and numbers not ending with 5.
Number Steps
74 50 + 24 = 74
52 = 25 Square the first digit (5) of first part (50) then add
= 25 + 24
= 49 second part (24)
242 = 576 Square the second part of number 24
49 + 576 = 5476 Add the answers got in step 1 (49)and step 2 (576)
Answer : 742 = 74 × 74 = 5476

Type 4: Squaring of number near to their base 10,100,1000, and so on:
Number Steps
105 100 + 5 = Divide the given number to their base and number
105 + 5 = 110 Add the second part of number 5 to the given number (105)
52 = 25 Square the second part of the 52
11025 Combine the numbers from step 1 and step 2
Answer : 1052 = 105 × 105 = 11025

Type 5: Squaring of a number near to their sub base:
Number Steps
306 300 + 6 = Divide the given number to their sub base and number

3 × (306 + 6)

= 3 ×312
= 936
Add the second part of number 6 to the given number (306) and multiply it by 3
62 = 36 Square the second part of the 62
93636 Combine the numbers from step 1 and step 2
Answer : 3062 = 306 × 306 = 93636


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Calculating Vedic Math Square Tricks can be classified in following types:

Yavadunam (Specific Method)
Ekadhikena Purvena (Specific Method)
DvandaYoga (General Method)

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