Fastest Technique to Find Square of Any Number | Vedic Maths
Vedic maths tricks are best suited for fast calculation and are very useful in calculation within seconds. Vedic maths tricks were discovered by ancient Indian Mathematicians so vedic maths techniques are of Indian Origin.
Square of numbers ending in 5 :
Sutra: ‘By one more than previous one”
Example: 75 × 75 or 752
As explained earlier in the chapter of multiplication we simply multiply 7 by the next number i.e. 8 to
get 56 which forms first part of answer and the last part is simply 25= (5)2
. So, 75 × 75 = 5625
This method is applicable to numbers of any size.
Example: 6052
60 × 61 = 3660 and 52
= 25
∴ 6052 = 366025
Square of numbers with decimals ending in 5
Example : (7.5)2
7 × 8 = 56, (0.52
) = 0.25
(7.5)2
= 56.25 (Similar to above example but with decimal)
Squaring numbers above 50:
Example: 522
Step1: First part is calculated as 52
+ 2 = 25 + 2 = 27
Step2: Last part is calculated as (2) 2 = 04 (two digits)
∴ 522 = 2704
Squaring numbers below 50
Example : 482
Step1: First part of answer calculated as: 52
– 2 = 25 – 2 = 23
Step2: second part is calculated as : 22
= 04
∴ 482
=2304
Squaring numbers near base :
Example : 10042
Step1: For first part add 1004and 04 to get 1008
Step2: For second part42
= 16 = 016 (as,base is 1000 a three digit no.)
∴ (1004)2
= 1008016
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2
Squaring numbers near sub - base:
Example (302)2
Step1: For first part = 3 (302 + 02) = 3 × 304 = 912 [Here sub – base is 300 so multiply by 3]
Step2: For second part = 22
= 04
∴ (302)2
= 91204
General method of squaring:
The Duplex
Sutra: “Single digit square, pair multiply and double” we will use the term duplex,` D’ as follows:
For 1 figure(or digit) Duplex is its squaree.g. D(4) = 42
= 16
For2 digitsDuplex is twice of the product e.g. D(34) = 2 (3 x 4) = 24
For 3 digit number: e.g. (341)2
D(3) = 32
= 9
D (34) = 2 (3 × 4) = 24
D (341) = 2 (3 × 1 ) + 42
= 6 + 16 = 22
9 4 2 8 1
D (41 ) = 2 (4 × 1 ) = 8 2 2
D (1) = 12
= 1 =116281
∴ (341)2
= 116281
Chapters:-
0:00 Vedic Maths Introduction
0:22 Square of 46
1:17 Square of 79
1:57 Square of 32
2:41 Questions
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