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50 cubed, (50)3, is the number you get when multiplying 50 times 50 times 50.
It can also be looked at as exponentiation involving the base 50 and the exponent 3.
The term is usually pronounced 3rd power of fifty or fifty cubed.
The cube of 50 is a perfect cube because the number is the product of the three equal integers 50.
It can be written as 50 × 50 × 50 or in exponential form.
Read on to learn everything about the number fifty cubed, including useful identities.
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50 × 50 × 50 = 125,000
The inverse operation of cubing 50 is extracting the cube root of 50, explained here.
In the next section we elaborate on the cube 50.
What is 50 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length 50 has an area of 125,000.
The sum and the differences of two cubes, for example with side length 50 and 49, can be calculated with the following formulas:
- a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 50, b = 49 and the equivalence we get:
(50)3 = 99 x (502 – 50 × 49 + 492) – 493 = 99 x (2500 – 2450 + 2401) – 117649 = 99 x 2451 – 117649 = 125,000 - a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 50, b = 49 and the equivalence we get:
(50)3 = (502 + 50 × 49 + 492) + 493 = 2500 + 2450 + 2401 + 117649 = 125,000
As follows from (1), 50 cubed can be calculated from 49 cubed and 50 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(50)3 = (2 × 50 – 1) × (502 – 50 + 1) – (49)3 = 99 × (2500 – 49) – 117649 = 99 × 2451 – 117649 = 125,000
Using the second formula 50 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(50)3 = 493 + 3 × 502 – 3 × 50 + 1 = 117649 + 3 × 2500 – 3 × 50 + 1 = 117649 + 7500 – 150 + 1 = 125,000
If you want to calculate the cube of any number, not only integers like 50, you can use our calculator above.
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A cube similar to 50 is, for example: cube of 52.
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The following table contains the cubes of numbers close to 50.
Table
| Number | Cube |
|---|---|
| 45 | 91,125 |
| 46 | 97,336 |
| 47 | 103,823 |
| 48 | 110,592 |
| 49 | 117,649 |
| 50 | 125,000 |
| 51 | 132,651 |
| 52 | 140,608 |
| 53 | 148,877 |
| 54 | 157,464 |
| 55 | 166,375 |
Fifty Cubed
You now know everything about the cube 50 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:
50 cubed is equivalent to 125,000.
If you were searching for what is 50 cubed in math or if you typed whats 50 cubed in the search engine you now have all the answers, too.
The same goes for searches like cube50, and 50 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 50 cubed using the search form in the sidebar of this page.
Ahead is the summary of our information.
Conclusion
To sum up,
50 cubed = 50 x 50 x 50 = (50)3 = 50 to the 3rd power = 125,000.
The exponentiation form is mostly used to denote 50 cube.
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– Article written by Mark, last updated on November 26th, 2023