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熟记11～25各整数的平方,是速算整数平方的基础。因而本文是在能熟记11～25各整数平方的基础上展开讨论的。一 25～100各整数的平方 1° 25～75各整数的平方 25～50的二位数可表示为50-a(a∈Z,且a≤25),a叫做该二位数对于50的补数; 50～75的二位数可表示为50+a(a∈Z,且a≤25),a叫做该二位数对于50的过数。 (50±a)~2,=50~2±2×50·a+a~2=2500±100a+a~2=(25±a)×100+a~2=〔(50±a)-25〕×100+a~2。上式说明:求25～75各整数的平方,可先求该数与25之差的100倍,再加上补数或过数的平方。
The square of each integer from 11 to 25 is used to know the base of the fast integer square. Therefore, this article is based on the ability to memorize 11 to 25 integer squares on the basis of discussion. A 25 to 100 square of each integer 1 25 to 75 integers 25 to 50 of the square of the two figures can be expressed as 50-a (a ∈ Z, and a ≤ 25), a is called the two-digit for 50 The complement number; The 50-75 two-digit number can be expressed as 50+a (a∈Z, and a≤25), and a is called the double digit for 50. (50±a)~2,=50~2±2×50·a+a~2=2500±100a+a~2=(25±a)×100+a~2=[(50±a)- 25〕×100+a~2. The formula above says: Find the square of the integer of 25-75, can first find the difference between the number and 25 times, plus the square of the complement or the excess.