Intresting Facts: 1. Difference between the squares of

Question

Intresting Facts:  

 1. Difference between the squares of numbers equidistant from 25 is in multiple of 100s.  

Example 

26^2 - 24^2 = 100 - Distance from 25 is 1 
27^2 - 23^2 = 200 - Distance from 25 is 2 
28^2 - 22^2 = 300 - Distance from 25 is 3 
29^2 - 21^2 = 400 - Distance from 25 is 4 
... 
... 
49^2 - 1^2 = 2400 - Distance from 25 is 24 

 2. Difference between the squares of numbers equidistant from 50 is in multiple of 200s . 

Example 

51^2 - 49^2 = 200 - Distance from 50 is 1 
52^2 - 48^2 = 400 - Distance from 50 is 2 
53^2 - 47^2 = 600 - Distance from 50 is 3 
54^2 - 46^2 = 800 - Distance from 50 is 4 
... 
... 
99^2 - 1^2 = 9800 - Distance from 50 is 49 

 3. Difference between the squares of numbers equidistant from 100 is in multiple of 400s. 

Example 

101^2 - 99^2 = 400 - Distance from 100 is 1 
102^2 - 98^2 = 800 - Distance from 100 is 2 
103^2 - 97^2 = 1200 - Distance from 100 is 3 
104^2 - 96^2 = 1600 - Distance from 100 is 4 
... 
... 
199^2 - 1^2 = 39600 - Distance from 100 is 99 

 4. Same way this is a series which goes on and on for numbers equidistant from 200 and then equidistant from 400 hundred etc etc.....

ps_dahiya · Answer

Finding squares of numbers from 26-50 

Requirement is to know squares of 1 to 25

Take example of 37.

Distance from 25 is 12 on upper side
Now number that is 12 points on the lower side of 25 is 13. So square of 37 is 12 * 100 + 13^2 = 1369

This may sound difficult but it is not.

Lets take another example of 48
Distance from 25 is 23 on the upper side
Now number that is 23 points on the lower side of 25 is 2. So square of 48 is 23*100 + 2^2 = 2304

How easy is that?

ps_dahiya · Answer

Finding Squares of numbers between 50 and 60 

Lets take 57.

Square (57) = ABCD
AB = Square of tenth digit (5) + Unit digit (7) = 25 + 7 = 32
CD = square of unit digit(7) = 49

So ABCD = 3249

ps_dahiya · Answer

Square of a number whose unit digit is 5 

Take example of 45^2 = ABCD

Multiply tenth digit and (tenth digit + 1) and then then put 25 in the end.
AB = 4* 5
CD = 25
So ABCD = 2025

This also applies to others like 125 ^2 = ABCDE

ABC = 12* 13 = 156
DE = 25
So ABCDE = 15625

ps_dahiya · Answer

Finding square of any number 

We will do it by example of 96

Steps:
1. Find a multiple of 10 nearest to 96 i.e 100
2. Is that multiple greater than 96 or lower than 96, and how much? If greater then subtract the difference from 96, if lower then add the difference to 96. Here we will add. i.e 96 - 4 = 92
3. Multiply the integer found in step 1 to step 2 i.e 9200
4. Add the square of difference found in step 2 i.e 4^2 = 16 i.e 9200 + 16 = 9616

I guarantee that this is a very easy method.

Suggestion: If you know the squares of 1 to 25 then its always advisable to find the nearest multiple a number so that multiplication with that multipe of 10 is easy.

For example, to find square of 82 you may find 80 as nearest multiple of 10 but why not take 100 as the nearest.

Then square of 82 is (82-18) * 100 + 324 = 6724

Don't think its difficult. Try it and then find yourself.

Bhai · Answer

Looks like you are doing Vedic Mathematics? That will save you a lot of time. :good

ps_dahiya · Answer

Squares of numbers having only digit 1: 

11^2 = 121
111^2 = 12321
1111^2 = 1234321
11111^2 = 123454321

and so on....

ps_dahiya · Answer

I did it in my high school. Just sharing with you guys. They are kind of printed in my mind since my old days.

sperumba · Answer

goodd job ps_dahiya. 

thanks,

sperumba · Answer

your squares rule directly follows from

x^2 -y^2 = (x+y) (x-Y)

26^2 - 24^2 = (26+24) (26-24) = 50 *2 = 100 - Distance from 25 is 1

allabout · Answer

Sum of consecutive squares  


The formula is n(n+1)(2n+1)/6.

Where n is the number of terms


For example:

What's the sum of the squares from 3^2 + 4^2 ... 15^2 ?

S(15) - S(2) = 1236

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Intresting Facts: 1. Difference between the squares of

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