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15 squared, (15)2, is the number you get when multiplying 15 times 15.
It can also be looked at as exponentiation involving the base 15 and the exponent 2.
The term is usually pronounced fifteen times fifteen or fifteen squared.
The square of 15 is a perfect square because the number is the product of the two equal integers 15.
It can be written as 15 × 15 or in exponential form.
Read on to learn everything about the number fifteen squared, including useful identities.
Calculator
(15)2 = 225
15 × 15 = 225
The inverse operation of squaring fifteen is extracting the square root of 15, explained here.
In the next section we elaborate on what is 15 squared and there you can also find our calculator.
What is 15 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 15 has an area of 225.
15 squared equals the sum of the first 15 odd numbers:
In addition, the number can be calculated from 14 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(15)2 = 142 + 14 + 15 = 142 + 29 = 225
It can be also be computed from 14 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(15)2 = 2 x 142 – 132 + 2 = 2 x 196 – 169 + 2 = 225
The difference between the perfect square of 15 and its predecessor, 14, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 15 – 1 = 29 = (15)2 – 142 = 225 – 196 = 29
15 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 15 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 15, you can use our calculator above.
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A square similar to 15 is, for example: square of 17.
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The following table contains the squares of numbers close to 15.
Table
| Number | Square |
|---|---|
| 10 | 100 |
| 11 | 121 |
| 12 | 144 |
| 13 | 169 |
| 14 | 196 |
| 15 | 225 |
| 16 | 256 |
| 17 | 289 |
| 18 | 324 |
| 19 | 361 |
| 20 | 400 |
Fifteen Squared
By reading so far you know all about squaring the number 15 and calculating it using recursive methods, or as sum, product or by exponentiation.
15 squared is equivalent to 225.
If you were searching for what is 15 squared in math or if you typed whats 15 squared in the search engine you now have all the answers, too.
The same goes for searches like square15, and 15 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 15 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
15 squared = 15 × 15 = (15)2 = 225.
The exponentiation form is mostly used to denote fifteen squared.
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– Article written by Mark, last updated on November 26th, 2023