289 Squared


289 squared, 2892, is the number you get when multiplying 289 times 289. It can also be looked at as exponentiation involving the base 289 and the exponent 2. The term is usually pronounced two hundred and eighty-nine times two hundred and eighty-nine or two hundred and eighty-nine squared. The square of 289 is a perfect square because the number is the product of the two equal integers 289. It can be written as 289 x 289 or in exponential form. Read on to learn everything about the number two hundred and eighty-nine squared, including the useful identities.

2892 = 83521
289 x 289 = 83521

The inverse operation of squaring two hundred and eighty-nine is extracting the square root of 289, explained here. In the next section we elaborate on what is 289 squared, and there you can also find our calculator.

What is 289 Squared

A square is a flat shape with four equal sides; every angle is 90°. Hence, a square with side length 289 has an area of 83521.

289 squared equals the sum of the first 289 odd numbers:

$\sum_{i=1}^{289} (2i-1)$ = 83521

In addition, the number can be calculated from 288 squared using the following identity:

n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
2892 = 2882 + 288 + 289 = 2882 + 577 = 83521

It can be also be computed from 288 squared with this identity:

n2 = 2 x (n − 1)2 − (n − 2)2 + 2
2892 = 2 x 2882 – 2872 + 2 = 2 x 82944 – 82369 + 2 = 83521

The difference between the perfect square of 289 and its predecessor, 288, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:

2 x 289 – 1 = 577 = 2892 – 2882 = 83521 – 82944 = 577

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

Squares of odd numbers like 289 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 289, 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 two hundred and eighty-nine, other squares on our site include, for instance:

289 Squared

Two Hundred And Eighty-Nine Squared

By reading so far you know all about squaring the number 289 and calculating it using recursive methods, or as sum, product or by exponentiation. 289 squared is equivalent to 83521.

If you were searching for what is 289 squared in math or if you typed whats 289 squared in the search engine, then you now have all the answers, too.

The same goes for searches like square289, and 289 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 289 squared using the search form in the sidebar and menu of this page.

To sum up,

289 squared = 289×289 = 2892 = 83521. The exponentiation form is mostly used to denote two hundred and eighty-nine squared.

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