991 Cubed

991 cubed, (991)³, is the number you get when multiplying 991 times 991 times 991.

It can also be looked at as exponentiation involving the base 991 and the exponent 3.

The term is usually pronounced 3rd power of nine hundred ninety-one or nine hundred ninety-one cubed.

The cube of 991 is a perfect cube because the number is the product of the three equal integers 991.

It can be written as 991 × 991 × 991 or in exponential form.

Read on to learn everything about the number nine hundred ninety-one cubed, including useful identities.

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(991)³ = 973,242,271
991 × 991 × 991 = 973,242,271
The inverse operation of cubing 991 is extracting the cube root of 991, explained here.

In the next section we elaborate on the cube 991.

What is 991 Cubed?

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

Hence, a cube with side length 991 has an area of 973,242,271.

The sum and the differences of two cubes, for example with side length 991 and 990, can be calculated with the following formulas:

1. a³ + b³ = (a + b) × (a² – ab + b²) ⇔ a³ = (a + b) × (a² – ab + b²) – b³
   With a = 991, b = 990 and the equivalence we get:
   (991)³ = 1981 x (991² – 991 × 990 + 990²) – 990³ = 1981 x (982081 – 981090 + 980100) – 970299000 = 1981 x 981091 – 970299000 = 973,242,271
2. a³ – b³ = (a – b) × (a² + ab + b²) ⇔ a³ = (a – b) × (a² + ab + b²) + b³
   With a = 991, b = 990 and the equivalence we get:
   (991)³ = (991² + 991 × 990 + 990²) + 990³ = 982081 + 981090 + 980100 + 970299000 = 973,242,271

As follows from (1), 991 cubed can be calculated from 990 cubed and 991 squared using the identity:

n³ = (2 × n – 1) × (n² -n + 1) – (n-1)³
(991)³ = (2 × 991 – 1) × (991² – 991 + 1) – (990)³ = 1981 × (982081 – 990) – 970299000 = 1981 × 981091 – 970299000 = 973,242,271

Using the second formula 991 cubed can be also be computed with this identity:

n³ = (n-1)³ + 3n² -3n + 1
(991)³ = 990³ + 3 × 991² – 3 × 991 + 1 = 970299000 + 3 × 982081 – 3 × 991 + 1 = 970299000 + 2946243 – 2973 + 1 = 973,242,271

If you want to calculate the cube of any number, not only integers like 991, you can use our calculator above.

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A cube similar to 991 is, for example: cube of 993.


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The following table contains the cubes of numbers close to 991.

Table

Nine Hundred Ninety-One Cubed

You now know everything about the cube 991 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:

991 cubed is equivalent to 973,242,271.

If you were searching for what is 991 cubed in math or if you typed whats 991 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube991, and 991 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 991 cubed using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

991 cubed = 991 x 991 x 991 = (991)³ = 991 to the 3rd power = 973,242,271.

The exponentiation form is mostly used to denote 991 cube.

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