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350 Cubed

350 cubed, (350)3, is the number you get when multiplying 350 times 350 times 350.

It can also be looked at as exponentiation involving the base 350 and the exponent 3.

The term is usually pronounced 3rd power of three hundred fifty or three hundred fifty cubed.

The cube of 350 is a perfect cube because the number is the product of the three equal integers 350.

It can be written as 350 × 350 × 350 or in exponential form.

Read on to learn everything about the number three hundred fifty cubed, including useful identities.

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(350)3 = 42,875,000
350 × 350 × 350 = 42,875,000

The inverse operation of cubing 350 is extracting the cube root of 350, explained here.

In the next section we elaborate on the cube 350.

What is 350 Cubed?

A cube is a three-dimensional shape with 6 equal square faces.

Hence, a cube with side length 350 has an area of 42,875,000.

The sum and the differences of two cubes, for example with side length 350 and 349, can be calculated with the following formulas:

  1. a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
    With a = 350, b = 349 and the equivalence we get:
    (350)3 = 699 x (3502 – 350 × 349 + 3492) – 3493 = 699 x (122500 – 122150 + 121801) – 42508549 = 699 x 122151 – 42508549 = 42,875,000
  2. a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
    With a = 350, b = 349 and the equivalence we get:
    (350)3 = (3502 + 350 × 349 + 3492) + 3493 = 122500 + 122150 + 121801 + 42508549 = 42,875,000

As follows from (1), 350 cubed can be calculated from 349 cubed and 350 squared using the identity:

n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(350)3 = (2 × 350 – 1) × (3502 – 350 + 1) – (349)3 = 699 × (122500 – 349) – 42508549 = 699 × 122151 – 42508549 = 42,875,000

Using the second formula 350 cubed can be also be computed with this identity:

n3 = (n-1)3 + 3n2 -3n + 1
(350)3 = 3493 + 3 × 3502 – 3 × 350 + 1 = 42508549 + 3 × 122500 – 3 × 350 + 1 = 42508549 + 367500 – 1050 + 1 = 42,875,000

If you want to calculate the cube of any number, not only integers like 350, you can use our calculator above.

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A cube similar to 350 is, for example: cube of 352.


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The following table contains the cubes of numbers close to 350.

Table

NumberCube
34541,063,625
34641,421,736
34741,781,923
34842,144,192
34942,508,549
35042,875,000
35143,243,551
35243,614,208
35343,986,977
35444,361,864
35544,738,875

Three Hundred Fifty Cubed

You now know everything about the cube 350 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:

350 cubed is equivalent to 42,875,000.

If you were searching for what is 350 cubed in math or if you typed whats 350 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube350, and 350 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 350 cubed using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

350 cubed = 350 x 350 x 350 = (350)3 = 350 to the 3rd power = 42,875,000.

The exponentiation form is mostly used to denote 350 cube.

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– Article written by Mark, last updated on November 26th, 2023