square of numbers in 100's

> Choose a number over 100 (START WITH SMALLER NUMBER).
> The last two places will be the square of
the last two digits (keep if any carry) _ _ _ X X.
> The first three places will be the number plus
the last two digits plus any carry: X X X _ _.

here is an Example:

> let the number be 108:
2. Square the last two digits (no carry): 8 × 8 = 64: _ _ _ 64
3. Add the last two digits to the number: 108 + 08= 116:
so 1 1 6 _ _
4. So 108 × 108 = 11664.

FIND SQUARE OF NUMBERS IN 200 TO 299

steps to find square of numbers in 200's

> Choose a number in the 200s (start with numbers under 210, then try for larger ones).
>The first digit of the square is 4: 4 _ _ _ _
> The next two digits will be 4 times the last 2 digits: _ X X _ _
> The last two places will be the square of the last digit: _ _ _ X X

here we take an Example:

> let the number be 207:
> The first digit is 4
so 4 _ _ _ _
> The next two digits are 4 times the last digit:
4 × 7 = 28
so _ 2 8 _ _
Square the last digit: 7× 7 = 49
so _ _ _ 49
So finally we get 206 × 206 = 42849.

and For larger numbers work right to left:

> Square the last two digits (keep the carry): _ _ _ X X
> 4 times the last two digits + carry: _ X X _ _
> Square the first digit + carry: X _ _ _ _

example

>If the number to be squared is 225:
> Square last two digits (keep carry):
25x25 = 625 (keep 6): _ _ _ 2 5
> 4 times the last two digits + carry:
4x25 = 100; 100+6 = 106 (keep 1): _ 0 6 _ _
> Square the first digit + carry:
2x2 = 4; 4+1 = 5: 5 _ _ _ _
> So 225 × 225 = 50625.

Square 2 Digit Number:WITH UP-DOWN Method

Square a 2 Digit Number, for this example 37:

> Look for the nearest 10 boundary
> In this case up 3 from 37 to 40.
> Since you went UP 3 to 40 go DOWN 3 from 37 to 34.
> Now mentally multiply 34x40
> The way I do it is 34x10=340;
> Double it mentally to 680
> Double it again mentally to 1360
> This 1360 is the FIRST interim answer.
> 37 is "3" away from the 10 boundary 40.
> Square this "3" distance from 10 boundary.
> 3x3=9 which is the SECOND interim answer.
> Add the two interim answers to get the final answer.
> Answer: 1360 + 9 = 1369

TO FIND SQUARE OF 3-DIGIT NUMBER

LET THE NUMBER BE ABC

SQ (ABC) is calculated like this

STEP 1. Last digit = last digit of SQ(C)
STEP 2. Second Last Digit = 2*B*C + any carryover from STEP 1.
STEP 3. Third Last Digit 2*A*C+ Sq(B) + any carryover from STEP
2.
STEP 4. Fourth last digit is 2*A*B + any carryover from STEP 3.
STEP 5 . In the beginning of result will be Sq(A) + any carryover
from Step 4.


EXAMPLE :

SQ (431)

STEP 1. Last digit = last digit of SQ(1) =1
STEP 2. Second Last Digit = 2*3*1 + any carryover from STEP
1.= 6
STEP 3. Third Last Digit 2*4*1+ Sq(3) + any carryover from STEP
2.= 2*4*1 +9= 17. so 7 and 1 carryover
STEP 4. Fourth last digit is 2*4*3 + any carryover (which is 1) . =
24+1=25. So 5 and carry over 2.
STEP 5 . In the beginning of result will be Sq(4) + any carryover
from Step 4. So 16+2 =18.

So the result will be 185761.