13 Squared

13 squared, (13)², is the number you get when multiplying 13 times 13.

It can also be looked at as exponentiation involving the base 13 and the exponent 2.

The term is usually pronounced thirteen times thirteen or thirteen squared.

The square of 13 is a perfect square because the number is the product of the two equal integers 13.

It can be written as 13 × 13 or in exponential form.

Read on to learn everything about the number thirteen squared, including useful identities.

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(13)² = 169
13 × 13 = 169
The inverse operation of squaring thirteen is extracting the square root of 13, explained here.

In the next section we elaborate on what is 13 squared and there you can also find our calculator.

What is 13 Squared?

A square is a flat shape with four equal sides; every angle is 90°.

Hence, a square with side length 13 has an area of 169.

13 squared equals the sum of the first 13 odd numbers:

In addition, the number can be calculated from 12 squared using the following identity:

n² = (n − 1)² + (n − 1) + n = (n − 1)² + (2n − 1)
(13)² = 12² + 12 + 13 = 12² + 25 = 169

It can be also be computed from 12 squared with this identity:

n² = 2 x (n − 1)² − (n − 2)² + 2
(13)² = 2 x 12² – 11² + 2 = 2 x 144 – 121 + 2 = 169

The difference between the perfect square of 13 and its predecessor, 12, can be calculated with the identity n² − (n − 1)² = 2n − 1:

2 x 13 – 1 = 25 = (13)² – 12² = 169 – 144 = 25

13 is odd, and the square numbers of odd numbers are also odd: (2n + 1)² = 4 × (n² + n) + 1.

Squares of odd numbers like 13 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 13, you can use our calculator above.

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A square similar to 13 is, for example: square of 15.


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The following table contains the squares of numbers close to 13.

Table

Thirteen Squared

By reading so far you know all about squaring the number 13 and calculating it using recursive methods, or as sum, product or by exponentiation.

13 squared is equivalent to 169.

If you were searching for what is 13 squared in math or if you typed whats 13 squared in the search engine you now have all the answers, too.

The same goes for searches like square13, and 13 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 13 squared using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

13 squared = 13 × 13 = (13)² = 169.

The exponentiation form is mostly used to denote thirteen squared.

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– Article written by Mark, last updated on November 26th, 2023