961 Squared

961 squared, (961)², is the number you get when multiplying 961 times 961.

It can also be looked at as exponentiation involving the base 961 and the exponent 2.

The term is usually pronounced nine hundred sixty-one times nine hundred sixty-one or nine hundred sixty-one squared.

The square of 961 is a perfect square because the number is the product of the two equal integers 961.

It can be written as 961 × 961 or in exponential form.

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

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(961)² = 923,521
961 × 961 = 923,521
The inverse operation of squaring nine hundred sixty-one is extracting the square root of 961, explained here.

In the next section we elaborate on what is 961 squared and there you can also find our calculator.

What is 961 Squared?

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

Hence, a square with side length 961 has an area of 923,521.

961 squared equals the sum of the first 961 odd numbers:

In addition, the number can be calculated from 960 squared using the following identity:

n² = (n − 1)² + (n − 1) + n = (n − 1)² + (2n − 1)
(961)² = 960² + 960 + 961 = 960² + 1921 = 923,521

It can be also be computed from 960 squared with this identity:

n² = 2 x (n − 1)² − (n − 2)² + 2
(961)² = 2 x 960² – 959² + 2 = 2 x 921600 – 919681 + 2 = 923,521

The difference between the perfect square of 961 and its predecessor, 960, can be calculated with the identity n² − (n − 1)² = 2n − 1:

2 x 961 – 1 = 1921 = (961)² – 960² = 923,521 – 921600 = 1921

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

Squares of odd numbers like 961 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 961, you can use our calculator above.

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A square similar to 961 is, for example: square of 963.


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The following table contains the squares of numbers close to 961.

Table

Nine Hundred Sixty-One Squared

By reading so far you know all about squaring the number 961 and calculating it using recursive methods, or as sum, product or by exponentiation.

961 squared is equivalent to 923,521.

If you were searching for what is 961 squared in math or if you typed whats 961 squared in the search engine you now have all the answers, too.

The same goes for searches like square961, and 961 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 961 squared using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

961 squared = 961 × 961 = (961)² = 923,521.

The exponentiation form is mostly used to denote nine hundred sixty-one squared.

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