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827 Squared

827 squared, (827)2, is the number you get when multiplying 827 times 827.

It can also be looked at as exponentiation involving the base 827 and the exponent 2.

The term is usually pronounced eight hundred twenty-seven times eight hundred twenty-seven or eight hundred twenty-seven squared.

The square of 827 is a perfect square because the number is the product of the two equal integers 827.

It can be written as 827 × 827 or in exponential form.

Read on to learn everything about the number eight hundred twenty-seven squared, including useful identities.

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(827)2 = 683,929
827 × 827 = 683,929
The inverse operation of squaring eight hundred twenty-seven is extracting the square root of 827, explained here.

In the next section we elaborate on what is 827 squared and there you can also find our calculator.

What is 827 Squared?

A square is a flat shape with four equal sides; every angle is 90°.

Hence, a square with side length 827 has an area of 683,929.

827 squared equals the sum of the first 827 odd numbers:


In addition, the number can be calculated from 826 squared using the following identity:

n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(827)2 = 8262 + 826 + 827 = 8262 + 1653 = 683,929

It can be also be computed from 826 squared with this identity:

n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(827)2 = 2 x 8262 – 8252 + 2 = 2 x 682276 – 680625 + 2 = 683,929

The difference between the perfect square of 827 and its predecessor, 826, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:

2 x 827 – 1 = 1653 = (827)2 – 8262 = 683,929 – 682276 = 1653

827 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.

Squares of odd numbers like 827 are of the form 8n + 1, because (2n + 1)2 = 4n × (n + 1) + 1;
n × (n + 1) is an even number.

If you want to calculate the square of any number, not only integers like 827, you can use our calculator above.

Enter your number; nothing else to be done.

A square similar to 827 is, for example: square of 829.


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The following table contains the squares of numbers close to 827.

Table

NumberSquare
822675,684
823677,329
824678,976
825680,625
826682,276
827683,929
828685,584
829687,241
830688,900
831690,561
832692,224

Eight Hundred Twenty-Seven Squared

By reading so far you know all about squaring the number 827 and calculating it using recursive methods, or as sum, product or by exponentiation.

827 squared is equivalent to 683,929.

If you were searching for what is 827 squared in math or if you typed whats 827 squared in the search engine you now have all the answers, too.

The same goes for searches like square827, and 827 to the 2nd power, just to name a few more examples people are often looking for.

Note that you can also find many perfect squares including 827 squared using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

827 squared = 827 × 827 = (827)2 = 683,929.

The exponentiation form is mostly used to denote eight hundred twenty-seven squared.

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– Article written by Mark, last updated on November 26th, 2023