997 Squared

997 squared, (997)², is the number you get when multiplying 997 times 997.

It can also be looked at as exponentiation involving the base 997 and the exponent 2.

The term is usually pronounced nine hundred ninety-seven times nine hundred ninety-seven or nine hundred ninety-seven squared.

The square of 997 is a perfect square because the number is the product of the two equal integers 997.

It can be written as 997 × 997 or in exponential form.

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

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(997)² = 994,009
997 × 997 = 994,009
The inverse operation of squaring nine hundred ninety-seven is extracting the square root of 997, explained here.

In the next section we elaborate on what is 997 squared and there you can also find our calculator.

What is 997 Squared?

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

Hence, a square with side length 997 has an area of 994,009.

997 squared equals the sum of the first 997 odd numbers:

In addition, the number can be calculated from 996 squared using the following identity:

n² = (n − 1)² + (n − 1) + n = (n − 1)² + (2n − 1)
(997)² = 996² + 996 + 997 = 996² + 1993 = 994,009

It can be also be computed from 996 squared with this identity:

n² = 2 x (n − 1)² − (n − 2)² + 2
(997)² = 2 x 996² – 995² + 2 = 2 x 992016 – 990025 + 2 = 994,009

The difference between the perfect square of 997 and its predecessor, 996, can be calculated with the identity n² − (n − 1)² = 2n − 1:

2 x 997 – 1 = 1993 = (997)² – 996² = 994,009 – 992016 = 1993

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

Squares of odd numbers like 997 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 997, you can use our calculator above.

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A square similar to 997 is, for example: square of 999.


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The following table contains the squares of numbers close to 997.

Table

Nine Hundred Ninety-Seven Squared

By reading so far you know all about squaring the number 997 and calculating it using recursive methods, or as sum, product or by exponentiation.

997 squared is equivalent to 994,009.

If you were searching for what is 997 squared in math or if you typed whats 997 squared in the search engine you now have all the answers, too.

The same goes for searches like square997, and 997 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 997 squared using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

997 squared = 997 × 997 = (997)² = 994,009.

The exponentiation form is mostly used to denote nine hundred ninety-seven squared.

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