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993 squared, (993)2, is the number you get when multiplying 993 times 993.
It can also be looked at as exponentiation involving the base 993 and the exponent 2.
The term is usually pronounced nine hundred ninety-three times nine hundred ninety-three or nine hundred ninety-three squared.
The square of 993 is a perfect square because the number is the product of the two equal integers 993.
It can be written as 993 × 993 or in exponential form.
Read on to learn everything about the number nine hundred ninety-three squared, including useful identities.
Calculator
(993)2 = 986,049
993 × 993 = 986,049
The inverse operation of squaring nine hundred ninety-three is extracting the square root of 993, explained here.
In the next section we elaborate on what is 993 squared and there you can also find our calculator.
What is 993 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 993 has an area of 986,049.
993 squared equals the sum of the first 993 odd numbers:
In addition, the number can be calculated from 992 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(993)2 = 9922 + 992 + 993 = 9922 + 1985 = 986,049
It can be also be computed from 992 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(993)2 = 2 x 9922 – 9912 + 2 = 2 x 984064 – 982081 + 2 = 986,049
The difference between the perfect square of 993 and its predecessor, 992, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 993 – 1 = 1985 = (993)2 – 9922 = 986,049 – 984064 = 1985
993 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 993 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 993, you can use our calculator above.
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A square similar to 993 is, for example: square of 995.
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The following table contains the squares of numbers close to 993.
Table
| Number | Square |
|---|---|
| 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 |
| 997 | 994,009 |
| 998 | 996,004 |
Nine Hundred Ninety-Three Squared
By reading so far you know all about squaring the number 993 and calculating it using recursive methods, or as sum, product or by exponentiation.
993 squared is equivalent to 986,049.
If you were searching for what is 993 squared in math or if you typed whats 993 squared in the search engine you now have all the answers, too.
The same goes for searches like square993, and 993 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 993 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
993 squared = 993 × 993 = (993)2 = 986,049.
The exponentiation form is mostly used to denote nine hundred ninety-three squared.
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– Article written by Mark, last updated on November 26th, 2023