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461 cubed, (461)3, is the number you get when multiplying 461 times 461 times 461.
It can also be looked at as exponentiation involving the base 461 and the exponent 3.
The term is usually pronounced 3rd power of four hundred sixty-one or four hundred sixty-one cubed.
The cube of 461 is a perfect cube because the number is the product of the three equal integers 461.
It can be written as 461 × 461 × 461 or in exponential form.
Read on to learn everything about the number four hundred sixty-one cubed, including useful identities.
Calculator
461 × 461 × 461 = 97,972,181
The inverse operation of cubing 461 is extracting the cube root of 461, explained here.
In the next section we elaborate on the cube 461.
What is 461 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length 461 has an area of 97,972,181.
The sum and the differences of two cubes, for example with side length 461 and 460, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 461, b = 460 and the equivalence we get:
(461)3 = 921 x (4612 – 461 × 460 + 4602) – 4603 = 921 x (212521 – 212060 + 211600) – 97336000 = 921 x 212061 – 97336000 = 97,972,181 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 461, b = 460 and the equivalence we get:
(461)3 = (4612 + 461 × 460 + 4602) + 4603 = 212521 + 212060 + 211600 + 97336000 = 97,972,181
As follows from (1), 461 cubed can be calculated from 460 cubed and 461 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(461)3 = (2 × 461 – 1) × (4612 – 461 + 1) – (460)3 = 921 × (212521 – 460) – 97336000 = 921 × 212061 – 97336000 = 97,972,181
Using the second formula 461 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(461)3 = 4603 + 3 × 4612 – 3 × 461 + 1 = 97336000 + 3 × 212521 – 3 × 461 + 1 = 97336000 + 637563 – 1383 + 1 = 97,972,181
If you want to calculate the cube of any number, not only integers like 461, you can use our calculator above.
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A cube similar to 461 is, for example: cube of 463.
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The following table contains the cubes of numbers close to 461.
Table
| Number | Cube |
|---|---|
| 456 | 94,818,816 |
| 457 | 95,443,993 |
| 458 | 96,071,912 |
| 459 | 96,702,579 |
| 460 | 97,336,000 |
| 461 | 97,972,181 |
| 462 | 98,611,128 |
| 463 | 99,252,847 |
| 464 | 99,897,344 |
| 465 | 100,544,625 |
| 466 | 101,194,696 |
Four Hundred Sixty-One Cubed
You now know everything about the cube 461 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
461 cubed is equivalent to 97,972,181.
If you were searching for what is 461 cubed in math or if you typed whats 461 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube461, and 461 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 461 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
461 cubed = 461 x 461 x 461 = (461)3 = 461 to the 3rd power = 97,972,181.
The exponentiation form is mostly used to denote 461 cube.
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– Article written by Mark, last updated on November 26th, 2023