Effortless Squaring with the Base Method!

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The square of numbers close to a base can be easily calculated using the formula: "Whatever the deficiency is, subtract that amount, and then add the square of the deficiency." This method simplifies squaring numbers that are close to a base number.

(98)2


The base number for 98 is 100.
Therefore, 100 - 98 = 02.
= 98 -02  |   2x2
= 96 | 04     (2 x 2 = 04)      ( where base is 100. )
= 9604

Step 1 : The number 98 is taken with a base of 100. The difference between 100 and 98 is 02. Subtract this difference from the given number to get the first part of the answer: 98 - 02 = 96.

Step 2 : Find the square of the difference (2² = 04). This forms the second part of the answer. Since the base is 100, the second part should be written as "04" to align with two decimal places.
Thus, the result is 9604.

(9999989)2


The base number for 9999989 is 10000000.
Therefore, 10000000 - 9999989 = 11.
= 9999989 - 11  |   11x11
= 9999978 | 121 (11 x 11 = 121)      ( where base is 100. )
= 9604

Step 1 : Take the number 9999989 with a base of 10000000. The difference between 10000000 and 9999989 is 11. Subtract this difference from the given number to get the first part of the answer: 9999989 - 11 = 9999978.

Step 2 : Calculate the square of the difference (11² = 121). This forms the second part of the answer. Append this to the first part to get the final answer: 9999978121.

(113)2=?


The base number for 113 is 100.
= 113 + 13  |  13 x 13
= 126 | 169     ( 13x13=169 where base is 100 )
= 126 | 169      ( Carry over (126+1=127 )
= 12769

Note that, until now, the numbers we've seen have been less than the base number. However, 113 is greater than the base number 100. Therefore, instead of subtracting the excess 13 from 113, we add it.

Step 1 : The number 113 has 100 as its base number. Therefore, the difference between 100 and 113 is 13. Add this 13 to the given number (113) to get the first part of the answer.(113 + 13 = 126).

Step 2 : Next, find the square of 13, which gives the second part of the answer. (13² = 169).
Note that the base number is 100, so from 169, we only take the last two digits (69) and carry forward the remainder (1). Thus, the final result is: 126 + 1 = 127.

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