123 Squared

123 squared, (123)², is the number you get when multiplying 123 times 123.

It can also be looked at as exponentiation involving the base 123 and the exponent 2.

The term is usually pronounced one hundred twenty-three times one hundred twenty-three or one hundred twenty-three squared.

The square of 123 is a perfect square because the number is the product of the two equal integers 123.

It can be written as 123 × 123 or in exponential form.

Read on to learn everything about the number one hundred twenty-three squared, including useful identities.

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(123)² = 15,129
123 × 123 = 15,129
The inverse operation of squaring one hundred twenty-three is extracting the square root of 123, explained here.

In the next section we elaborate on what is 123 squared and there you can also find our calculator.

What is 123 Squared?

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

Hence, a square with side length 123 has an area of 15,129.

123 squared equals the sum of the first 123 odd numbers:

In addition, the number can be calculated from 122 squared using the following identity:

n² = (n − 1)² + (n − 1) + n = (n − 1)² + (2n − 1)
(123)² = 122² + 122 + 123 = 122² + 245 = 15,129

It can be also be computed from 122 squared with this identity:

n² = 2 x (n − 1)² − (n − 2)² + 2
(123)² = 2 x 122² – 121² + 2 = 2 x 14884 – 14641 + 2 = 15,129

The difference between the perfect square of 123 and its predecessor, 122, can be calculated with the identity n² − (n − 1)² = 2n − 1:

2 x 123 – 1 = 245 = (123)² – 122² = 15,129 – 14884 = 245

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

Squares of odd numbers like 123 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 123, you can use our calculator above.

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A square similar to 123 is, for example: square of 125.


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The following table contains the squares of numbers close to 123.

Table

One Hundred Twenty-Three Squared

By reading so far you know all about squaring the number 123 and calculating it using recursive methods, or as sum, product or by exponentiation.

123 squared is equivalent to 15,129.

If you were searching for what is 123 squared in math or if you typed whats 123 squared in the search engine you now have all the answers, too.

The same goes for searches like square123, and 123 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 123 squared using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

123 squared = 123 × 123 = (123)² = 15,129.

The exponentiation form is mostly used to denote one hundred twenty-three squared.

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