123 Squared


123 squared, 1232, 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 hundred and twenty-three times hundred and twenty-three or hundred and 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 x 123 or in exponential form. Read on to learn everything about the number hundred and twenty-three squared, including the useful identities.

1232 = 15129
123 x 123 = 15129

The inverse operation of squaring hundred and 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 15129.

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

$\sum_{i=1}^{123} (2i-1)$ = 15129

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)
1232 = 1222 + 122 + 123 = 1222 + 245 = 15129

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

n2 = 2 x (n − 1)2 − (n − 2)2 + 2
1232 = 2 x 1222 – 1212 + 2 = 2 x 14884 – 14641 + 2 = 15129

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 = 1232 – 1222 = 15129 – 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 below. Just insert your number; the calculation is done automatically.

Calculate Squared Number

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If this tool has been valuable to you, then bookmark it now. Besides the square of hundred and twenty-three, other squares on our site include, for instance:

123 Squared

Hundred And 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 15129.

If you were searching for what is 123 squared in math or if you typed whats 123 squared in the search engine, then 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 and menu of this page.

To sum up,

123 squared = 123×123 = 1232 = 15129. The exponentiation form is mostly used to denote hundred and twenty-three squared.

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