Table of Contents
12 squared, (12)2, is the number you get when multiplying 12 times 12.
It can also be looked at as exponentiation involving the base 12 and the exponent 2.
The term is usually pronounced twelve times twelve or twelve squared.
The square of 12 is a perfect square because the number is the product of the two equal integers 12.
It can be written as 12 × 12 or in exponential form.
Read on to learn everything about the number twelve squared, including useful identities.
Calculator
(12)2 = 144
12 × 12 = 144
The inverse operation of squaring twelve is extracting the square root of 12, explained here.
In the next section we elaborate on what is 12 squared and there you can also find our calculator.
What is 12 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 12 has an area of 144.
12 squared equals the sum of the first 12 odd numbers:
In addition, the number can be calculated from 11 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(12)2 = 112 + 11 + 12 = 112 + 23 = 144
It can be also be computed from 11 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(12)2 = 2 x 112 – 102 + 2 = 2 x 121 – 100 + 2 = 144
The difference between the perfect square of 12 and its predecessor, 11, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 12 – 1 = 23 = (12)2 – 112 = 144 – 121 = 23
12 is even, and the square numbers of even numbers are also even: (2n)2 = 4n2.
Squares of even numbers like 12 are divisible by 4 for
= n2.
If you want to calculate the square of any number, not only integers like 12, you can use our calculator above.
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A square similar to 12 is, for example: square of 14.
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The following table contains the squares of numbers close to 12.
Table
| Number | Square |
|---|---|
| 7 | 49 |
| 8 | 64 |
| 9 | 81 |
| 10 | 100 |
| 11 | 121 |
| 12 | 144 |
| 13 | 169 |
| 14 | 196 |
| 15 | 225 |
| 16 | 256 |
| 17 | 289 |
Twelve Squared
By reading so far you know all about squaring the number 12 and calculating it using recursive methods, or as sum, product or by exponentiation.
12 squared is equivalent to 144.
If you were searching for what is 12 squared in math or if you typed whats 12 squared in the search engine you now have all the answers, too.
The same goes for searches like square12, and 12 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 12 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
12 squared = 12 × 12 = (12)2 = 144.
The exponentiation form is mostly used to denote twelve squared.
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– Article written by Mark, last updated on November 26th, 2023