square root of seventh power of 57
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Answer:
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A square is a flat shape with four equal sides; every angle is 90°.
Hence, a squar e with side length 57 has an area of 3249.
57 squared equals the sum of the first 57 odd numbers:
\sum_{i=1}^{57} (2i-1) = 3249
In addition, the number can be calculated from 56 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
572 = 562 + 56 + 57 = 562 + 113 = 3249
It can be also be computed from 56 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
572 = 2 x 562 – 552 + 2 = 2 x 3136 – 3025 + 2 = 3249
The difference between the perfect square of 57 and its predecessor, 56, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 57 – 1 = 113 = 572 – 562 = 3249 – 3136 = 113
57 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 57 are of the form 8n + 1, because (2n + 1)2 = 4n × (n + 1) + 1;
n × (n + 1) is an even number.
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