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991 squared, (991)2, is the number you get when multiplying 991 times 991.
It can also be looked at as exponentiation involving the base 991 and the exponent 2.
The term is usually pronounced nine hundred ninety-one times nine hundred ninety-one or nine hundred ninety-one squared.
The square of 991 is a perfect square because the number is the product of the two equal integers 991.
It can be written as 991 × 991 or in exponential form.
Read on to learn everything about the number nine hundred ninety-one squared, including useful identities.
Calculator
(991)2 = 982,081
991 × 991 = 982,081
The inverse operation of squaring nine hundred ninety-one is extracting the square root of 991, explained here.
In the next section we elaborate on what is 991 squared and there you can also find our calculator.
What is 991 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 991 has an area of 982,081.
991 squared equals the sum of the first 991 odd numbers:
In addition, the number can be calculated from 990 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(991)2 = 9902 + 990 + 991 = 9902 + 1981 = 982,081
It can be also be computed from 990 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(991)2 = 2 x 9902 – 9892 + 2 = 2 x 980100 – 978121 + 2 = 982,081
The difference between the perfect square of 991 and its predecessor, 990, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 991 – 1 = 1981 = (991)2 – 9902 = 982,081 – 980100 = 1981
991 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 991 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 991, you can use our calculator above.
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A square similar to 991 is, for example: square of 993.
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The following table contains the squares of numbers close to 991.
Table
| Number | Square |
|---|---|
| 986 | 972,196 |
| 987 | 974,169 |
| 988 | 976,144 |
| 989 | 978,121 |
| 990 | 980,100 |
| 991 | 982,081 |
| 992 | 984,064 |
| 993 | 986,049 |
| 994 | 988,036 |
| 995 | 990,025 |
| 996 | 992,016 |
Nine Hundred Ninety-One Squared
By reading so far you know all about squaring the number 991 and calculating it using recursive methods, or as sum, product or by exponentiation.
991 squared is equivalent to 982,081.
If you were searching for what is 991 squared in math or if you typed whats 991 squared in the search engine you now have all the answers, too.
The same goes for searches like square991, and 991 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 991 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
991 squared = 991 × 991 = (991)2 = 982,081.
The exponentiation form is mostly used to denote nine hundred ninety-one squared.
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– Article written by Mark, last updated on November 26th, 2023