Table of Contents
19 squared, (19)2, is the number you get when multiplying 19 times 19.
It can also be looked at as exponentiation involving the base 19 and the exponent 2.
The term is usually pronounced nineteen times nineteen or nineteen squared.
The square of 19 is a perfect square because the number is the product of the two equal integers 19.
It can be written as 19 × 19 or in exponential form.
Read on to learn everything about the number nineteen squared, including useful identities.
Calculator
(19)2 = 361
19 × 19 = 361
The inverse operation of squaring nineteen is extracting the square root of 19, explained here.
In the next section we elaborate on what is 19 squared and there you can also find our calculator.
What is 19 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 19 has an area of 361.
19 squared equals the sum of the first 19 odd numbers:
In addition, the number can be calculated from 18 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(19)2 = 182 + 18 + 19 = 182 + 37 = 361
It can be also be computed from 18 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(19)2 = 2 x 182 – 172 + 2 = 2 x 324 – 289 + 2 = 361
The difference between the perfect square of 19 and its predecessor, 18, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 19 – 1 = 37 = (19)2 – 182 = 361 – 324 = 37
19 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 19 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 19, you can use our calculator above.
Enter your number; nothing else to be done.
A square similar to 19 is, for example: square of 21.
If something remains unclear do not hesitate getting in touch with us.
We are constantly trying to improve our site, and truly appreciate your feedback.
The following table contains the squares of numbers close to 19.
Table
| Number | Square |
|---|---|
| 14 | 196 |
| 15 | 225 |
| 16 | 256 |
| 17 | 289 |
| 18 | 324 |
| 19 | 361 |
| 20 | 400 |
| 21 | 441 |
| 22 | 484 |
| 23 | 529 |
| 24 | 576 |
Nineteen Squared
By reading so far you know all about squaring the number 19 and calculating it using recursive methods, or as sum, product or by exponentiation.
19 squared is equivalent to 361.
If you were searching for what is 19 squared in math or if you typed whats 19 squared in the search engine you now have all the answers, too.
The same goes for searches like square19, and 19 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 19 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
19 squared = 19 × 19 = (19)2 = 361.
The exponentiation form is mostly used to denote nineteen squared.
If this article about the square of 19 has been of help to you then please share it by means of the social buttons.
And should you want to leave a comment related to 19 squared use the form below.
Websites which are related to this one can be found in the “recommended sites” section in the sidebar.
Last, but not least, don’t forget to install our absolutely free PWA app (see menu or sidebar), or to bookmark us.
And come back soon!
Thanks for your visit.
– Article written by Mark, last updated on November 26th, 2023