Table of Contents
81 squared, (81)2, is the number you get when multiplying 81 times 81.
It can also be looked at as exponentiation involving the base 81 and the exponent 2.
The term is usually pronounced eighty-one times eighty-one or eighty-one squared.
The square of 81 is a perfect square because the number is the product of the two equal integers 81.
It can be written as 81 × 81 or in exponential form.
Read on to learn everything about the number eighty-one squared, including useful identities.
Calculator
(81)2 = 6,561
81 × 81 = 6,561
The inverse operation of squaring eighty-one is extracting the square root of 81, explained here.
In the next section we elaborate on what is 81 squared and there you can also find our calculator.
What is 81 Squared?
A square is a flat shape with four equal sides; every angle is 90°.
Hence, a square with side length 81 has an area of 6,561.
81 squared equals the sum of the first 81 odd numbers:
In addition, the number can be calculated from 80 squared using the following identity:
n2 = (n − 1)2 + (n − 1) + n = (n − 1)2 + (2n − 1)
(81)2 = 802 + 80 + 81 = 802 + 161 = 6,561
It can be also be computed from 80 squared with this identity:
n2 = 2 x (n − 1)2 − (n − 2)2 + 2
(81)2 = 2 x 802 – 792 + 2 = 2 x 6400 – 6241 + 2 = 6,561
The difference between the perfect square of 81 and its predecessor, 80, can be calculated with the identity n2 − (n − 1)2 = 2n − 1:
2 x 81 – 1 = 161 = (81)2 – 802 = 6,561 – 6400 = 161
81 is odd, and the square numbers of odd numbers are also odd: (2n + 1)2 = 4 × (n2 + n) + 1.
Squares of odd numbers like 81 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 81, you can use our calculator above.
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A square similar to 81 is, for example: square of 83.
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The following table contains the squares of numbers close to 81.
Table
| Number | Square |
|---|---|
| 76 | 5,776 |
| 77 | 5,929 |
| 78 | 6,084 |
| 79 | 6,241 |
| 80 | 6,400 |
| 81 | 6,561 |
| 82 | 6,724 |
| 83 | 6,889 |
| 84 | 7,056 |
| 85 | 7,225 |
| 86 | 7,396 |
Eighty-One Squared
By reading so far you know all about squaring the number 81 and calculating it using recursive methods, or as sum, product or by exponentiation.
81 squared is equivalent to 6,561.
If you were searching for what is 81 squared in math or if you typed whats 81 squared in the search engine you now have all the answers, too.
The same goes for searches like square81, and 81 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 81 squared using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
81 squared = 81 × 81 = (81)2 = 6,561.
The exponentiation form is mostly used to denote eighty-one squared.
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– Article written by Mark, last updated on November 26th, 2023