Tell Me How To Find Squares Of Numbers Ending in all nos except 5 using Vedic Maths?

Question

If u can please tell me atleast the method of finding out squares of numbers ending in all numbers except 5 because I already have 5. If u cant tell all please tell atleast some

Answer 1

I guess that you know squaring of numbers ending as 5!

It is an easy manner but it also misguides a user a bit!

Better you raised a question on subject matter!

Vedic Mathematics primarily compute huge digits numbers!

Squaring is an important Vedic computing! Technically it is a multiplying of "same digits numbers"! A few digits, or more digits or a huge number of digits number can be squared! They are three different categories!

Small numbers (0...9 ) may be memorized

Numbers 11...99 may be related as zero-start 2D square matrix row-column (merged yx positions of 0...9 row -col numbers)

Easiest 2 digits numbers for squaring are

50+/- a-unit steps (say 40 ...60) have squares...

40...1600
41...1681
42...1764
43...1849
44...1936
45...2025
46...2116
47...2209
48...2304
49...2401

50...2500

51...2601
52...2704
53...2809
54...2916
55...3025
56...3136
57...3249
58...3364
59...3481
60...3600

You know a method 55^2 =(5*6)---> 30/25 <---(5*5)!

You may use a general method for all numbers given above!

Take base number 50 and 50^2 = 5^2---> 25/00 <---0^2

For numbers less than 50...,49^2= 25-1--->24/01 <--- (-1)^2

For numbers less than 50...,48^2= 25-2--->23/04 <--- (-2)^2

For numbers less than 50...,47^2= 25-3--->22/09 <--- (-3)^2


For numbers more than 50...,51^2= 25+1--->26/01 <--- (1)^2

For numbers more than 50...,52^2= 25+2--->27/04 <--- (2)^2

For numbers more than 50...,53^2= 25+3--->28/09 <--- (3)^2


You can also follow said method by relating to base number 100+/- a unit step numbers but manner changes a bit

For numbers less than 100...,99^2= 99-1--->98/01 <--- (-1)^2

For numbers less than 100...,98^2= 98-2--->96/04 <--- (-2)^2

For numbers less than 100...,97^2= 97-3--->94/09 <--- (-3)^2

and so on...

For more than 100...,101^2= 101+1--->102/01 <--- (1)^2

For more than 100...,102^2= 102+2--->104/04 <--- (2)^2

For more than 100...,103^2= 103+3--->106/09 <--- (3)^2


In said manner we can apply reasonably more digits numbers squaring!

By dividing or multiplying said numbers by 4 we can extend squaring to other numbers

Example is 40^2 =1600 and 1600/4= 400= 20^2
Example is 41^2 =1681 and 1681*4= 6724= 82^2 and so on!

However, a classic example of squaring relates a sutra nikhilam navatascaramam dasata: (all from nine and last from 10, which relates a respective digits sum adding of two equal digits pair of numbers)

1/81 = 01234567,9 recurring digits alone!
80/81=98765432,1 recurring digits alone!
>>>>>-----------------
...........99999999,10 this is meaning of sutra!(It is respective digits sum when added vertically, 9th digits, 8th digits etc...)

We can merge digits as 012345679,987654321 which is square of (111111111)^2.

Answer of 1^2, 11^2, 111^2 etc also can be merged from either side of merged reciprocals as equal digits!

You may also extend said application to (222222222)^2 by merging 4/81 and (81-4)/81 or similar pair of complementary reciprocals!

You may also extend it to higher order numbers like....

00 01 02 03 04 05 06 ....93 94 95 96 97 99 (skip 2 nd last)
99 98 97 96 95 94 93.....06 05 04 03 02 01.

You can merge it as a 396 digits answer and it is exact square of (99 times 01)!

You have tried two digits groups and any higher digits work like this!

Guess what a Vedic Mathematician can do?


Regards!

Answer 2

Method 1
Called as I X I method
e.g.
2 3
×
2 3
Right side I means 3 × 3 = 9 write 9 in units place
middle X = 3 × 2 + 3 × 2 = 12 write 2 in 10's place and 1 c/f to 100's place.
Left I means 2 × 2 = 4
4 + 1 = 5 write in 100's place
Answer is 529

Method 2 called as Ganesh Method.
Draw square with 2 rows and 2 columns.
Draw diagonals in each square, from bottom left. it is difficult explain here. but try it
write 2 3 on the first row of square. and 2 3 on outside of right of square.
multiply 3 × 2 = 06 write in the second column as 0 on the above the diagonal and 6 below the diagonal in 1st row of 2nd column.
multiply 2 × 2 = 04 write in the first column as 0 on the above the diagonal and 6 below the diagonal in 1st row of 1st column.
multiply 3 × 3 = 09 write in the second column as 0 on the above the diagonal and 9 below the diagonal in 2nd row of 2nd column.
multiply 2 × 3 = 06 write in the first column as 0 on the above the diagonal and 6 below the diagonal in 2nd row of 2nd column.
Add digits in slanting way. answer is 529
This method can be used in any multiplications with any no. of digits. not necessary the square.
For that you have to draw square or rectangle depending on multiple and multiplicand.

Answer 3

ya suppose u have to find the square of 96

96
x96

here we'll go like this.....vertically...then cross...then again vertically

1) vertically----6*6 is 36......write 6 n carry 3
2) cross----- 6*9 is 54 and 9*6 is 54....54+54 is 108
108+3=111....now write 1 n carry 11
3) vertically-----9*9 is 81
81+11=92
write 92

so now u get 9216

this was to give u a rough idea......
its given in more detailed form in http://www.ilovemaths.com

Answer 4

Do not take no as ending with no 5

Answer 5

our method of squaring nos near 50 is as follows:
for eg:
46*46=
,rounding upwards,50*50=2500.we take 50 nd 2500 as reference pts..
46--> is 4 less than 50 ,so we take 4.it is a minus no.
i.e we take 4 frm d no of number hundreds in 2500.
25-4=21. tis is no of100's in answer.our subtotal is 2100.
to get rest of d answer,we square the minus no.
i.e. 4*4=16
so 2100+16=2116.


another eg: 56*56=
56is more than 50 so 6 more than 50.
so we add 6 to the no of 100's in 2500.
i.e.25+6=31.our subtotal is 3100
then square 6....6*6=36
so ans is 3136...


similarly for soqaring nos near 500 we take 500 nd 250,000 as reference pts...


for nos ending in 1:
eg: 31*31=
1st subtract 1 frm d no..so the no ends in zero..
i.e . 30*30=900.
2nd add 30+31=61.
then add ths to our subtotal,900,
so 900+61=961...




i hope so u woould understand it.......

Answer 6

search google for vedic math

Answer 7

ask a maths teacher