LEARN THE TRICKS OF VEDIC MATHS How to square numbers faster By UTKARSH UJUWAL

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Please remember this 2 22- 4 32- 9 42= 16 5 25 62-36 72-49 82 64 92- 81 102 = 100 112 121 122-144 132 169 142 196 152 225 162 256 172 289 182= 324 192 361 202- 400 212 = 441 222 = 484 232 529 242-576 252 625 262 676 272 729 282 784 292 841 302 900

Some specific cases: If the numberends with 5 as the unit s digit: .If the number ends with 5 as the unit's digit Eg: Suppose the number is a 5 (For 185, a= 13) (a 5ax (a+1)/25 a X (a Square Multiply a with 25 next digit

Examples: 35 (3 x 4)/25-1225 752 = (7 x 8) / 25-56 25 2= (7x 1152 -(11 x 12)/25 13225 1452=(14x15) / 25-21025

Calculating squares using algebraic identities 1. (a + b)2 a2 + b2 + 2ab (a + 1)2=a2 + a + (a + 1) (a-1 )2-2-a-(a-1) (a + 2)2 = a2 + 4 (a + 1) (a-2)2 = a2-4(a-1) : 362-(35 + 1)2=(352 +35 + 36) = 1225 + 71-1296 : 692 = (70-1)2 = (702-70-69)-4900-139-4761 : 322 (30 + 2)2 = 302 + 4(31)-900 + 124-1024 > : 782-(80-2) 2-802-4(79)-6400-316-6084 And so o

2. a2-(a b) (a+ b) b2 1042 100 x 108 + 42-108 16 (a-104, b = 4) 422 40 x 44 22 1764 372 34 x 4032 1369

3. (50 a)2-100 (25 a) + a2 For numbers close to 50 use given trick (a + 25)a (a + 25) / Eg: 542 p Consider 50 as base 29 / 16 As 54 (50+ 4) here a 4 542 = 100 (25 + 4) + 42 = 2900 + 16 = 2916

(100 a)2= 100 (100 2a) + a2 Can you visualise what to do ?? 103 100 (100 + 6) 32 106/09 - 106 09

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Utkarsh Ujjwal

A third year undergraduate at IIT Guwahati.. A NTSE scholar, KVPY fellow, multi Olympiad winner and a Mathematics lover at heart..

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Dheeraj Singh Baisla

2 years ago

very helpful

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S

Sowjanya

9 months ago

in 54^2 =(5^2+4)/4^2=29/16=2916 can v solve like this

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Shubham Malik

3 years ago

First of all I want to say ur videos are helpful. Thankyou so much. And I want to ask if u can help in better observation skills in series questions in quantitative aptitude? I never crack it's trick. Almost 5 questions will come in an upcoming exam in ibps clerks. So it will be great if u can help :)

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Alla Ramyasree

3 years ago

can i know again how 37^2 has calculated ? Please explain anyone??

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Utkarsh Ujjwal

3 years ago

Take a = 37 and b = 3 . (34 x 40) is fairly simple to get.

SR

Sagar Rajora

3 years ago

37^2
09 49
now multiply 3×7=21 and double it 42
now,
09 49
+4 2|
---------------
13 69
ans= 1369

Shamili S

3 years ago

The aim is to get a multiple of 10 to make the calc easier.
a^2= (a+b) (a-b)+b^2
So, you can take a=37, to find 37^2.
Now to make it a multiple of 10, you can use b=7 or 3 ( 37-7 =30 or 37+3 =40)
As b= 3 has already been explained, I will use b= 7
So, 37^2= 44*30 + 49
= 1320+49 = 1369; using 3 will be easier though :)

Manoj mohan

2 years ago

you are very fast can't catch up

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Utkarsh Ujjwal

2 years ago

Watch the same course by me in Hindi. I have explained a bit slowly in that course :)

Anish Ranjan Jal

3 years ago

For 37sq you took a = 37 and b = 3 . But why is 'b' taken as 3 I couldn't understand that.

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Pratyush Ranjan

3 years ago

For 'b' we assume a number closest to 10. So as for 37, 40 is closest and the difference of 40-37=3 so b=3