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.