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17 squared, (17)2, is the number you get when multiplying 17 times 17.
It can also be looked at as exponentiation involving the base 17 and the exponent 2.
The term is usually pronounced seventeen times seventeen or seventeen squared.
The square of 17 is a perfect square because the number is the product of the two equal integers 17.
It can be written as 17 × 17 or in exponential form.
Read on to learn everything about the number seventeen squared, including useful identities.
Calculator
(17)2 = 289
17 × 17 = 289
The inverse operation of squaring seventeen is extracting the square root of 17, explained here.
In the next section we elaborate on what is 17 squared and there you can also find our calculator.
What is 17 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 17 has an area of 289.
17 squared equals the sum of the first 17 odd numbers:
In addition, the number can be calculated from 16 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(17)2 = 162 + 16 + 17 = 162 + 33 = 289
It can be also be computed from 16 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(17)2 = 2 x 162 – 152 + 2 = 2 x 256 – 225 + 2 = 289
The difference between the perfect square of 17 and its predecessor, 16, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 17 – 1 = 33 = (17)2 – 162 = 289 – 256 = 33
17 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 17 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 17, you can use our calculator above.
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A square similar to 17 is, for example: square of 19.
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The following table contains the squares of numbers close to 17.
Table
| Number | Square |
|---|---|
| 12 | 144 |
| 13 | 169 |
| 14 | 196 |
| 15 | 225 |
| 16 | 256 |
| 17 | 289 |
| 18 | 324 |
| 19 | 361 |
| 20 | 400 |
| 21 | 441 |
| 22 | 484 |
Seventeen Squared
By reading so far you know all about squaring the number 17 and calculating it using recursive methods, or as sum, product or by exponentiation.
17 squared is equivalent to 289.
If you were searching for what is 17 squared in math or if you typed whats 17 squared in the search engine you now have all the answers, too.
The same goes for searches like square17, and 17 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 17 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
17 squared = 17 × 17 = (17)2 = 289.
The exponentiation form is mostly used to denote seventeen squared.
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– Article written by Mark, last updated on November 26th, 2023