Find 90's square using the proximity method(method to find squares between 75-125).
Find 90's square using the proximity method(method to find squares between 75-125).
Use following method for calculating squares of numbers from 76 to 125 :
a) Select a number ‘x’ ranging from 76 and 105.
Example: x = 121
b) Find difference of this number from 100 i.e. y = +|x – 100|. This difference would lie between -25 and 25.
Example: y = (121 – 100) = 21
c) Find square of this difference. y2 = (x – 100)2. Last two digits of this square would form the first and second place digits from right in the final square. Any third digit of this square would be carried forward to the hundreth place.
Example: y2 = (21)2 = 441
In the example, 41 would form the last two digits of the final square while 4 would be carried over to third digit from right.
d) Add the difference to the number itself i.e. z = x + y. This can also be written as z = (100 + 2y)
Ones and tens place digit of this number will form the third and fourth digit from right of the final square. Any third digit of this number would be carried forward to fifth place.
Example: z = 121 + 21 = 142 or z = 100 + (2*21) = 142
Here, 42 will form the thousands and hundreds digits of the final square. 1 will be carried forward as fifth digit
e) Bring together the first two and last two digits of the final square i.e. _z_ _y2_
Example: 142+441 = 14641
Use following method for calculating squares of numbers from 76 to 125 :
a) Select a number ‘x’ ranging from 76 and 105.
Example: x = 121
b) Find difference of this number from 100 i.e. y = +|x – 100|. This difference would lie between -25 and 25.
Example: y = (121 – 100) = 21
c) Find square of this difference. y2 = (x – 100)2. Last two digits of this square would form the first and second place digits from right in the final square. Any third digit of this square would be carried forward to the hundreth place.
Example: y2 = (21)2 = 441
In the example, 41 would form the last two digits of the final square while 4 would be carried over to third digit from right.
d) Add the difference to the number itself i.e. z = x + y. This can also be written as z = (100 + 2y)
Ones and tens place digit of this number will form the third and fourth digit from right of the final square. Any third digit of this number would be carried forward to fifth place.
Example: z = 121 + 21 = 142 or z = 100 + (2*21) = 142
Here, 42 will form the thousands and hundreds digits of the final square. 1 will be carried forward as fifth digit
e) Bring together the first two and last two digits of the final square i.e. _z_ _y2_
Example: 142+441 = 14641
