997 Squared


997 squared, 9972, 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 and ninety-seven times nine hundred and ninety-seven or nine hundred and 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 x 997 or in exponential form. Read on to learn everything about the number nine hundred and ninety-seven squared, including the useful identities.

9972 = 994009
997 x 997 = 994009

The inverse operation of squaring nine hundred and 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 994009.

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

$\sum_{i=1}^{997} (2i-1)$ = 994009

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)
9972 = 9962 + 996 + 997 = 9962 + 1993 = 994009

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

n2 = 2 x (n − 1)2 − (n − 2)2 + 2
9972 = 2 x 9962 – 9952 + 2 = 2 x 992016 – 990025 + 2 = 994009

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 = 9972 – 9962 = 994009 – 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 below. Just insert your number; the calculation is done automatically.

Calculate Squared Number

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If this tool has been valuable to you, then bookmark it now. Besides the square of nine hundred and ninety-seven, other squares on our site include, for instance:

997 Squared

Nine Hundred And 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 994009.

If you were searching for what is 997 squared in math or if you typed whats 997 squared in the search engine, then 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 and menu of this page.

To sum up,

997 squared = 997×997 = 9972 = 994009. The exponentiation form is mostly used to denote nine hundred and ninety-seven squared.

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