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11 squared, (11)2, is the number you get when multiplying 11 times 11.
It can also be looked at as exponentiation involving the base 11 and the exponent 2.
The term is usually pronounced eleven times eleven or eleven squared.
The square of 11 is a perfect square because the number is the product of the two equal integers 11.
It can be written as 11 × 11 or in exponential form.
Read on to learn everything about the number eleven squared, including useful identities.
Calculator
(11)2 = 121
11 × 11 = 121
The inverse operation of squaring eleven is extracting the square root of 11, explained here.
In the next section we elaborate on what is 11 squared and there you can also find our calculator.
What is 11 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 11 has an area of 121.
11 squared equals the sum of the first 11 odd numbers:
In addition, the number can be calculated from 10 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(11)2 = 102 + 10 + 11 = 102 + 21 = 121
It can be also be computed from 10 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(11)2 = 2 x 102 – 92 + 2 = 2 x 100 – 81 + 2 = 121
The difference between the perfect square of 11 and its predecessor, 10, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 11 – 1 = 21 = (11)2 – 102 = 121 – 100 = 21
11 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 11 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 11, you can use our calculator above.
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A square similar to 11 is, for example: square of 13.
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The following table contains the squares of numbers close to 11.
Table
| Number | Square |
|---|---|
| 6 | 36 |
| 7 | 49 |
| 8 | 64 |
| 9 | 81 |
| 10 | 100 |
| 11 | 121 |
| 12 | 144 |
| 13 | 169 |
| 14 | 196 |
| 15 | 225 |
| 16 | 256 |
Eleven Squared
By reading so far you know all about squaring the number 11 and calculating it using recursive methods, or as sum, product or by exponentiation.
11 squared is equivalent to 121.
If you were searching for what is 11 squared in math or if you typed whats 11 squared in the search engine you now have all the answers, too.
The same goes for searches like square11, and 11 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 11 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
11 squared = 11 × 11 = (11)2 = 121.
The exponentiation form is mostly used to denote eleven squared.
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– Article written by Mark, last updated on November 26th, 2023