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81 cubed, (81)3, is the number you get when multiplying 81 times 81 times 81.
It can also be looked at as exponentiation involving the base 81 and the exponent 3.
The term is usually pronounced 3rd power of eighty-one or eighty-one cubed.
The cube of 81 is a perfect cube because the number is the product of the three equal integers 81.
It can be written as 81 × 81 × 81 or in exponential form.
Read on to learn everything about the number eighty-one cubed, including useful identities.
Calculator
81 × 81 × 81 = 531,441
The inverse operation of cubing 81 is extracting the cube root of 81, explained here.
In the next section we elaborate on the cube 81.
What is 81 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length 81 has an area of 531,441.
The sum and the differences of two cubes, for example with side length 81 and 80, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 81, b = 80 and the equivalence we get:
(81)3 = 161 x (812 – 81 × 80 + 802) – 803 = 161 x (6561 – 6480 + 6400) – 512000 = 161 x 6481 – 512000 = 531,441 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 81, b = 80 and the equivalence we get:
(81)3 = (812 + 81 × 80 + 802) + 803 = 6561 + 6480 + 6400 + 512000 = 531,441
As follows from (1), 81 cubed can be calculated from 80 cubed and 81 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(81)3 = (2 × 81 – 1) × (812 – 81 + 1) – (80)3 = 161 × (6561 – 80) – 512000 = 161 × 6481 – 512000 = 531,441
Using the second formula 81 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(81)3 = 803 + 3 × 812 – 3 × 81 + 1 = 512000 + 3 × 6561 – 3 × 81 + 1 = 512000 + 19683 – 243 + 1 = 531,441
If you want to calculate the cube of any number, not only integers like 81, you can use our calculator above.
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A cube similar to 81 is, for example: cube of 83.
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The following table contains the cubes of numbers close to 81.
Table
| Number | Cube |
|---|---|
| 76 | 438,976 |
| 77 | 456,533 |
| 78 | 474,552 |
| 79 | 493,039 |
| 80 | 512,000 |
| 81 | 531,441 |
| 82 | 551,368 |
| 83 | 571,787 |
| 84 | 592,704 |
| 85 | 614,125 |
| 86 | 636,056 |
Eighty-One Cubed
You now know everything about the cube 81 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
81 cubed is equivalent to 531,441.
If you were searching for what is 81 cubed in math or if you typed whats 81 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube81, and 81 to the 3rd power, just to name a few more examples people are often looking for.
Note that you can also find many perfect cubes including 81 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
81 cubed = 81 x 81 x 81 = (81)3 = 81 to the 3rd power = 531,441.
The exponentiation form is mostly used to denote 81 cube.
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– Article written by Mark, last updated on November 26th, 2023