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Home Q & A Board Science-Related Homework Help Mathematics
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juliaroberts juliaroberts
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11 years ago
There is a trick solving double digit exponents (ex. 52^2) and something with the number 50. Does anyone know? If so, how do you solve all other double digits under 30, or above 70?
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#1
11 years ago
The only trick I know is an accelerator:

(a + b) = a^2 + 2 * a * b + b^2

for a=50
the term   2 * a * b  will always be 100 * b.

Try with 57
2500
+700 since 100 * b = 700
+49
total 3249

The recipe is:
-- square the first digit
-- add the second digit
-- append 2 zero
-- add the square of the second digit.

try with 59 (the worst case)
25
34
3400
3481

 try with 53
25
28
2800
2809
wrote...
#2
11 years ago
what do you want?
59^2 = ? working base 50 = 100/2
59 + 9
59 + 9
---------------
(59 + 9) / 2 and (9)*(9) = 3481 answer

23^2 = ? working base 20 = 10*2
23 + 3
23 + 3
---------------
(23 + 3)*2 and (3)(3) = 529

78^2 = ? working base = 70 = 10*7
78 + 8
78 + 8
--------------
(78 + 8)*7 and (8)(8) = 602 and 64 = 6084
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