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343 cubed, (343)3, is the number you get when multiplying 343 times 343 times 343.
It can also be looked at as exponentiation involving the base 343 and the exponent 3.
The term is usually pronounced 3rd power of three hundred forty-three or three hundred forty-three cubed.
The cube of 343 is a perfect cube because the number is the product of the three equal integers 343.
It can be written as 343 × 343 × 343 or in exponential form.
Read on to learn everything about the number three hundred forty-three cubed, including useful identities.
Calculator
343 × 343 × 343 = 40,353,607
The inverse operation of cubing 343 is extracting the cube root of 343, explained here.
In the next section we elaborate on the cube 343.
What is 343 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length 343 has an area of 40,353,607.
The sum and the differences of two cubes, for example with side length 343 and 342, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 343, b = 342 and the equivalence we get:
(343)3 = 685 x (3432 – 343 × 342 + 3422) – 3423 = 685 x (117649 – 117306 + 116964) – 40001688 = 685 x 117307 – 40001688 = 40,353,607 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 343, b = 342 and the equivalence we get:
(343)3 = (3432 + 343 × 342 + 3422) + 3423 = 117649 + 117306 + 116964 + 40001688 = 40,353,607
As follows from (1), 343 cubed can be calculated from 342 cubed and 343 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(343)3 = (2 × 343 – 1) × (3432 – 343 + 1) – (342)3 = 685 × (117649 – 342) – 40001688 = 685 × 117307 – 40001688 = 40,353,607
Using the second formula 343 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(343)3 = 3423 + 3 × 3432 – 3 × 343 + 1 = 40001688 + 3 × 117649 – 3 × 343 + 1 = 40001688 + 352947 – 1029 + 1 = 40,353,607
If you want to calculate the cube of any number, not only integers like 343, you can use our calculator above.
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A cube similar to 343 is, for example: cube of 345.
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The following table contains the cubes of numbers close to 343.
Table
| Number | Cube |
|---|---|
| 338 | 38,614,472 |
| 339 | 38,958,219 |
| 340 | 39,304,000 |
| 341 | 39,651,821 |
| 342 | 40,001,688 |
| 343 | 40,353,607 |
| 344 | 40,707,584 |
| 345 | 41,063,625 |
| 346 | 41,421,736 |
| 347 | 41,781,923 |
| 348 | 42,144,192 |
Three Hundred Forty-Three Cubed
You now know everything about the cube 343 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
343 cubed is equivalent to 40,353,607.
If you were searching for what is 343 cubed in math or if you typed whats 343 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube343, and 343 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 343 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
343 cubed = 343 x 343 x 343 = (343)3 = 343 to the 3rd power = 40,353,607.
The exponentiation form is mostly used to denote 343 cube.
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– Article written by Mark, last updated on November 26th, 2023