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289 squared, (289)2, is the number you get when multiplying 289 times 289.
It can also be looked at as exponentiation involving the base 289 and the exponent 2.
The term is usually pronounced two hundred eighty-nine times two hundred eighty-nine or two hundred eighty-nine squared.
The square of 289 is a perfect square because the number is the product of the two equal integers 289.
It can be written as 289 × 289 or in exponential form.
Read on to learn everything about the number two hundred eighty-nine squared, including useful identities.
Calculator
(289)2 = 83,521
289 × 289 = 83,521
The inverse operation of squaring two hundred eighty-nine is extracting the square root of 289, explained here.
In the next section we elaborate on what is 289 squared and there you can also find our calculator.
What is 289 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 289 has an area of 83,521.
289 squared equals the sum of the first 289 odd numbers:
In addition, the number can be calculated from 288 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(289)2 = 2882 + 288 + 289 = 2882 + 577 = 83,521
It can be also be computed from 288 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(289)2 = 2 x 2882 – 2872 + 2 = 2 x 82944 – 82369 + 2 = 83,521
The difference between the perfect square of 289 and its predecessor, 288, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 289 – 1 = 577 = (289)2 – 2882 = 83,521 – 82944 = 577
289 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 289 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 289, you can use our calculator above.
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A square similar to 289 is, for example: square of 291.
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The following table contains the squares of numbers close to 289.
Table
| Number | Square |
|---|---|
| 284 | 80,656 |
| 285 | 81,225 |
| 286 | 81,796 |
| 287 | 82,369 |
| 288 | 82,944 |
| 289 | 83,521 |
| 290 | 84,100 |
| 291 | 84,681 |
| 292 | 85,264 |
| 293 | 85,849 |
| 294 | 86,436 |
Two Hundred Eighty-Nine Squared
By reading so far you know all about squaring the number 289 and calculating it using recursive methods, or as sum, product or by exponentiation.
289 squared is equivalent to 83,521.
If you were searching for what is 289 squared in math or if you typed whats 289 squared in the search engine you now have all the answers, too.
The same goes for searches like square289, and 289 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 289 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
289 squared = 289 × 289 = (289)2 = 83,521.
The exponentiation form is mostly used to denote two hundred eighty-nine squared.
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– Article written by Mark, last updated on November 26th, 2023