SQUARING TRICK -: 3rd

Note -: when we want to square any number then we also apply another method which is as follows :
 Take an example -: 116^2 ?

Step (1).  Multiply unit digit of the given number with 2 . (6×2 = 12)

Step (2). Now multiply the given number with the number which is two times of unit digit. (116×12)

Step (3). Find the square of unit digit of the given number. (6^2 = 36 = 6×6)

Step (4). Now subtract the square of unit digit from the number which comes in step second . {( 116×12 )- 36} = 1356.

Step (5). Square the number which is  multiple of 10 comes before the given number . if 116 is given then the multiple of 10 before it is 110. (110^2 = 12100)

Step (6). Now add the numbers which we find in step '4' and step '5' , which is the answer of square of the given number .
(1356+12100 = 13456).

So , 116^2 = 13456 will be the answer..

Question(1) -: 118^2 ?

Answer -:
step(a) . unit digit is 8 in this question so ,multiply  it with two  -: 8 × 2  = 16

Step(b) . multiply the double (the answer which comes in step a) of unit digit with the
 given number -: 118 × 16= 1888

Step(c) . square the unit digit of the given number  which is 8 -: 8^2 = 64

Step(d) . now subtract the answer of step c (64) from step b (1888) -: 1888 - 64 = 1824 .

Step(e) . square the number which is multiple of 10 which comes before the given  number. 110 is the number which is multiple of 10 and come before 118 -: 110^2 = 12100.

Step( f). Now add the resultant numbers of step 'd' (1824) and 'e'(12100) -:
1824 + 12100 = 13924 .

Question -: 239 ^ 2 ?

Answer -: step (a) -: 9×2 = 18.
Step (b). 239 ×18 = 4302
Step (c). 9^2 = 81
Step (d). 4302 - 81 = 4221.
Step(e .  230^2 = 52900
Step ( f) . 52900 + 4221 = 57121
Answer willbe 57121.

Question -: 523×523(523^2) ?
Answer -: step(a). 3×2 = 6
Step(b). 523×6 = 3138
Step(c). 3×3 (3^2) = 9
Step(d). 3138 - 9 = 3129
Step(e). 520^2 = 270400
Step(f). 270400 + 3129 = 273529
Hence ans will be 273529.

Question -: 2782 ^ 2 ?
Answer -: step(a).2×2 = 4 (here unit digit number is 2 which is multiply with 2)
Step(b). 2782×4 = 11128
Step(c). 2^2 = 4
Step(d). 11128 - 4 = 11124
Step(e).2780^2 = 7728400
Step(f). 7728400 + 11124 = 7739524
Answer will be 7739524.

                                       SQUARING TRICK

Note -: As we see below , the symbol  " ^ " comes every where .what is the use of this symbol ?
Answer -: The use of this symbol (" ^ " ) is to raise the power of any number like
26^2 = 26×26 ( 26 raise to the power 2)
48^2 =  48×48
579^2 = 579×579
6978^ 2 = 6978 × 6978
6978^3 = 6978×6978× 6978 ( 6978 raise to the power 3)
6978^5 = 6978×6978×6978×6978×6978 (6978 raise to the power 5)

Type 1st -:

(1) Find the answer of  -: 36^2

Procedure  -: step (1) . square the one's digit of the given number  .
6^2 = 36 . (36^2 =     6)

Step(2). Multiply one's and tenth digit of the given number to each other and then multiply it with 2.
(3×6)×2 = 36 .
Now add carry over 3 from 36 to 36
= 36 + 3 = 39.    (36^2 =      96)

Step (3) . square the tenth digit of the given number .
3^2 = 9.
Now add 3 (carry over from 39) to 9
= 9 + 3 = 12 .   (36^2 = 1296)
Answer -: will be 1296 .

Note -: By applying this method we can solve the square of any number without written work within seconds

Question (2) -: Find the result of 582^2.

Step (1). Square the ones digit of the given number  = 2^2  = 4 = 2×2
Step (2) . multiply ones and tenth digit of the given number and then multiply it by 2
= (8×2)×2 = 32   { 582^2 =         24}

Step (3) .  multiply ones and hundredth digit of the given number to each other, and then multiply it with 2 ,  and then add square of tenth digit to it   -
= { (5×2)×2 + ( 8^2) } = { 20 + 64 } = 84 .
Now add carry over 3 from 32 to 84  -
84 + 3 = 87 .    { 582^2 =      724}

Step (4) . Multiply tenth and hundredth digit of number to each other and then multiply it with 2 -
(5×8)×2 = 80 .
Now add carry over 8 from 87 to 42
= 80 + 8 = 88 {582^2 =   8724 }

Step ( 5) . square the value of hundredth of the given number
 5^2 = 25
Now add  8 from 88 to 25 .
 25+8 = 33 .
The answer become -: 338724.
.
Question (3) -:Find the value of  4248^2.

Answer -:
step (1) -: 8^2 = 64         {4248^2 =       4}

Step (2) -: (4×8)×2 = 64
Add 6 ( carryover ) from 64 to 64= 64+6 = 70
{4248^2 =      04}

Step(3) -: {(2×8)×2 }+ (4^2) = 48
Add carryover 7 to 48 = 48+7= 55.
 {4248^2 =    504}

Step(4) -: {(4×8)×2} +{ (2×4)×2} = 80
Add 5 (carryover from 55) to 80 = 5+80 = 85
{4248^2 =   5504}

Step (5) -:{ (4×4)×2}+(2^2) = 36
Add 8 (carryover from 85) to 36 = 36+8 = 44
{ 4248^2 =   45504}

Step(6) -: (4×2)×2 = 16
Add 4 (carryover from 44) to 16 = 16+4 = 20
{ 4248^2 =    045504}

Step(7) -: 4^2 = 16
Add 2 (carryover from 20) to 16 = 16+2 = 18
{4248^2 = 18045504}
So the answer of 4248^2 = 18045504.

                      MULTIPLY TRICk
Note-; when we multiply two number , Remembered that every number multiply to each other at ones .
 Note -: this is also vedic method .

Type (1) -:

(a) . Find the answer -:   26×12

Answer-:
step 1. Multiply ones digit of these numbers , mean to say -
 6×2 = 12.    { 26×12=       2}

Step 2 . multiply ones digit of 26 to tens digit of 12 and tens digit of 26 to ones digit of 12 and add the resultants -
(6×1)+(2×2) = 10
 Now add  1(carry over from 12) to 10
1+10=11 .  {26×12=        12}

Step 3. Multiply tenth digit of these number
              2×1= 2
 Add 1 ( carry over from 11) to this result
 2+1 = 3 .  { 26×12 = 312}

Answer -: will be 312.

(b) . find the answer -: 79×13
Answer -:
Step 1. 9×3 = 27   {79×12 =     7}
Step 2. (9×1) + (7×3) = 30
Now , add 2 (carry cover from 27) to 30
30+2= 32 .   { 79×13=    27}
Step 3 . 7× 1 = 7
Now add 3 (carry over from 32) to 7
7+3=10 .  { 1027}

Answer -: will be 1027.

Type (2) -: find the result -: 378×27 .

Answer -: step 1 . 8×7 = 56.   { 378 ×27 =     6}

Step 2 . (7×7) + ( 8×2) = 65
Now ,add 5 ( carry over from 56) to 65
65+5 = 70 .   { 378 × 27 =            06}

Step 3. (7×3) + (2×7) =  35
now, add 7 to 35
35 + 7 = 42 .    { 378×27 =      206}

Step 4 . 2×3 = 6
now add 4 to 6
 4+6 = 10 .  { 378 × 27 = 10206}

Answer-: will be 10206

Type (3) -: Find the result of 376×482

Answer -: step (1) . 6×2 = 12 .  (376×482 =    2)

                  Step(2). (6×8) + (7×2) = 62
Now add 1(carryover from 12) to 62
= 62 + 1 = 63 .   (376×482 =          32)

                  Step (3). (3×2) + (6×4) +(7×8) = 86
Now add 6 (carry over from 62) to 86
      = 6 + 86 = 92. (376×482 =        232)

               Step(4). (3×8) + (7×4) = 52
Now add 9 (carry over ) to 52
    = 52 + 9 = 61 . (376×482 =       1232)

         Step(5). 3×4 = 12 .
Now add 6 (carry over from 61) to 12
         = 12+6 = 18 .  (376×482 = 181232 )

Answer -: 376 × 482 = 181232.

Note -: we see that every number from 376 and 482 multiply to each other at ones time .