sponsored links

^{2 }= 1225 Here 3 x 4 = 12 so the answer is 1225

45

^{2 }= 2025
55

^{2 }= 3025
75

^{2 }= 5625
95

^{2 }= 9025
125

^{2 }= 15625
175

^{2 }= 30625
235

^{2 }= 55225
195

^{2 }= 38025
245

^{2 }= 60025
Well friends, now we know the squares of numbers 25, 30, 35, 40, 45, 50, 55 etc. If we want to find the squares of any other number, we find it using these squares which we already know.

For 262 we will go from 252, for 322 we go from 30 2 and so on.

One way is writing 262 = (25+1)2. But we need not even calculate (a+b)2 by adopting the following method.

262 = 252 + 26th odd number. i.e., 625 + 51 = 676

(a+b)2 = a2 + 2ab + b2

262 = (25 + 1 )2

= 252 + 2 x 25 x 1 + 12

= 625 + 50 + 1

= 625 + 51

= 676

So, the answer is same. Now we shall look at an easiest method which will help you to calculate Squares Mentally.

12 = 1 = 1

2 2 = 4 = 1+3

32 = 9 = 1+ 3 + 5

42 = 16 = 1 + 3 + 5 + 7

52 = 25 = 1 + 3 + 5 + 7 + 9

I mean, to get n2, you should add the FIRST n odd numbers. If we want 172, it will be the sum of the FIRST 17 odd numbers.

**n**

^{th }odd number is equal to (2n - 1)
Suppose you want to find out 62 knowing what 52 is, we can move from 52 to 62.

62 will be the sum of 1st 6 odd numbers. But the sum of the first 6 odd numbers can be written as " Sum of the first 5 odd numbers" + "Sixth odd number". Since we already know that the sum of the FIRST 5 odd numbers is 52 , i.e., 25, we need to add the sixth odd number, i mean (2x 6-1) = 11 to 25 to give us 62 = 36.

Similarly

312 = 900 + 31st Odd number = 900 + 61 = 961

362 = 1225 + 36th odd number = 1225 + 71

= 1296
(remember that 352 = 1225)

412 = 1600 + 81 = 1681

462 = 2025 + 91 = 2116

1262 = 15625 + 251 = 15876

1962 = 38025 + 391 = 38416

2162 = 46225 + 461 = 46656 Read More ☛

**Don't forget to LIKE our Facebook page here for daily Math Shortcut Tips**sponsored links

excellent

ReplyDeletepretty good and easy one.. thanks for the contribution

ReplyDeletethank you...:)

ReplyDeletedo any type of square

ReplyDeletelet's take (74)^2=5476

(7)^2=49

(4)^2=16

7*4*2=56 so write as 4 9 1 6

5 6

---- -------

5 4 7 6

another ex (109)^2=11881

first square of 10=100

then square of 9=81

10*9*2=180

1 0 0 8 1

1 8 0

----------

1 1 8 8 1

Thank you so much for the comment Prag Kamra

DeleteGood Day :)

Thanks Prag,

Deleteexcellent Prag Kamra...

Deletebut in last step how are you adding the number plz elaborate ot

Deletewhat a trick salute u sir G.ese hi hume gyan dete rahiye

Deletebut we cant find the square of 123,243 by this techniq please guide

DeleteBut according to prag kamra we cant find the square of 123 like many number please guide

Deletewe cant find square of 123 by dat method pls explain

Deletewe can find d square of 123 by dat method..

Deletelook

123 => 12 & 3

now(12)^2 = 144 & 3^2 = 09

so, 14409

now 2*12*3=72

14409

+72

15129. here is the answer..

As i did it like

Delete216 => 2 &16

2^2=4 & 16^2=256

so 4256

thn 2*2*16=64

4256

+64

4896

bt answer shud be 46656

Hw will you calculate the last step like 10081 and 180. Kindly clarify that one.

Deleteit takes time so better for everyone to remember at least 50

ReplyDeleteNice. . .

ReplyDeletethank you

ReplyDeleteTHANKU YAR .......THIS IS NICE TRICK..........

ReplyDeleteIts truely useful for all i will surely share this site with my friends

ReplyDeleteimpressive.. (y)

ReplyDeleteSimply superb

ReplyDeletesimply superb..

ReplyDeletecool... thx sir...

ReplyDeletemethod of prag is also nice one. thanks prag.

ReplyDeleten mam i have a doubt in last method. if we need sq of 37 then, acording to (35)^2 + 37th term the answer is not comming correct..

look now a combination of mam n prag method.

ReplyDeletewhat if given term is large like 329 or 412.

we dnt knw sq of 32 or 41. but we know d short method.

32^2= 04

12

9

adding in this manner what we get. 1024

what is the sq of 9. its 81.

so numbr comes as told by prag 102481.

now what we have to ad 2*32*9. cant we do this?

576? right.

102481

576

108241.

yo done it.. chk it now.. n enjoy.. all the sq of 3digit numbers u have now before a minute. jst practice.

look now a combination of mam n prag method.

ReplyDeletewhat if given term is large like 329 or 412.

we dnt knw sq of 32 or 41. but we know d short method.

32^2= 04

12

9

adding in this manner what we get. 1024

what is the sq of 9. its 81.

so numbr comes as told by prag 102481.

now what we have to ad 2*32*9. cant we do this?

576? right.

102481

576

108241.

yo done it.. chk it now.. n enjoy.. all the sq of 3digit numbers u have now before a minute. jst practice.