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450 cubed, (450)3, is the number you get when multiplying 450 times 450 times 450.
It can also be looked at as exponentiation involving the base 450 and the exponent 3.
The term is usually pronounced 3rd power of four hundred fifty or four hundred fifty cubed.
The cube of 450 is a perfect cube because the number is the product of the three equal integers 450.
It can be written as 450 × 450 × 450 or in exponential form.
Read on to learn everything about the number four hundred fifty cubed, including useful identities.
Calculator
450 × 450 × 450 = 91,125,000
The inverse operation of cubing 450 is extracting the cube root of 450, explained here.
In the next section we elaborate on the cube 450.
What is 450 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length 450 has an area of 91,125,000.
The sum and the differences of two cubes, for example with side length 450 and 449, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 450, b = 449 and the equivalence we get:
(450)3 = 899 x (4502 – 450 × 449 + 4492) – 4493 = 899 x (202500 – 202050 + 201601) – 90518849 = 899 x 202051 – 90518849 = 91,125,000 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 450, b = 449 and the equivalence we get:
(450)3 = (4502 + 450 × 449 + 4492) + 4493 = 202500 + 202050 + 201601 + 90518849 = 91,125,000
As follows from (1), 450 cubed can be calculated from 449 cubed and 450 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(450)3 = (2 × 450 – 1) × (4502 – 450 + 1) – (449)3 = 899 × (202500 – 449) – 90518849 = 899 × 202051 – 90518849 = 91,125,000
Using the second formula 450 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(450)3 = 4493 + 3 × 4502 – 3 × 450 + 1 = 90518849 + 3 × 202500 – 3 × 450 + 1 = 90518849 + 607500 – 1350 + 1 = 91,125,000
If you want to calculate the cube of any number, not only integers like 450, you can use our calculator above.
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A cube similar to 450 is, for example: cube of 452.
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The following table contains the cubes of numbers close to 450.
Table
| Number | Cube |
|---|---|
| 445 | 88,121,125 |
| 446 | 88,716,536 |
| 447 | 89,314,623 |
| 448 | 89,915,392 |
| 449 | 90,518,849 |
| 450 | 91,125,000 |
| 451 | 91,733,851 |
| 452 | 92,345,408 |
| 453 | 92,959,677 |
| 454 | 93,576,664 |
| 455 | 94,196,375 |
Four Hundred Fifty Cubed
You now know everything about the cube 450 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
450 cubed is equivalent to 91,125,000.
If you were searching for what is 450 cubed in math or if you typed whats 450 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube450, and 450 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 450 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
450 cubed = 450 x 450 x 450 = (450)3 = 450 to the 3rd power = 91,125,000.
The exponentiation form is mostly used to denote 450 cube.
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– Article written by Mark, last updated on November 26th, 2023