997 Cubed

997 cubed, (997)³, is the number you get when multiplying 997 times 997 times 997.

It can also be looked at as exponentiation involving the base 997 and the exponent 3.

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

The cube of 997 is a perfect cube because the number is the product of the three equal integers 997.

It can be written as 997 × 997 × 997 or in exponential form.

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

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(997)³ = 991,026,973
997 × 997 × 997 = 991,026,973
The inverse operation of cubing 997 is extracting the cube root of 997, explained here.

In the next section we elaborate on the cube 997.

What is 997 Cubed?

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

Hence, a cube with side length 997 has an area of 991,026,973.

The sum and the differences of two cubes, for example with side length 997 and 996, can be calculated with the following formulas:

1. a³ + b³ = (a + b) × (a² – ab + b²) ⇔ a³ = (a + b) × (a² – ab + b²) – b³
   With a = 997, b = 996 and the equivalence we get:
   (997)³ = 1993 x (997² – 997 × 996 + 996²) – 996³ = 1993 x (994009 – 993012 + 992016) – 988047936 = 1993 x 993013 – 988047936 = 991,026,973
2. a³ – b³ = (a – b) × (a² + ab + b²) ⇔ a³ = (a – b) × (a² + ab + b²) + b³
   With a = 997, b = 996 and the equivalence we get:
   (997)³ = (997² + 997 × 996 + 996²) + 996³ = 994009 + 993012 + 992016 + 988047936 = 991,026,973

As follows from (1), 997 cubed can be calculated from 996 cubed and 997 squared using the identity:

n³ = (2 × n – 1) × (n² -n + 1) – (n-1)³
(997)³ = (2 × 997 – 1) × (997² – 997 + 1) – (996)³ = 1993 × (994009 – 996) – 988047936 = 1993 × 993013 – 988047936 = 991,026,973

Using the second formula 997 cubed can be also be computed with this identity:

n³ = (n-1)³ + 3n² -3n + 1
(997)³ = 996³ + 3 × 997² – 3 × 997 + 1 = 988047936 + 3 × 994009 – 3 × 997 + 1 = 988047936 + 2982027 – 2991 + 1 = 991,026,973

If you want to calculate the cube of any number, not only integers like 997, you can use our calculator above.

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A cube similar to 997 is, for example: cube of 999.


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The following table contains the cubes of numbers close to 997.

Table

Nine Hundred Ninety-Seven Cubed

You now know everything about the cube 997 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities:

997 cubed is equivalent to 991,026,973.

If you were searching for what is 997 cubed in math or if you typed whats 997 cubed in the search engine you now have all the answers, too.

The same goes for searches like cube997, and 997 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 997 cubed using the search form in the sidebar of this page.

Ahead is the summary of our information.

Conclusion

To sum up,

997 cubed = 997 x 997 x 997 = (997)³ = 997 to the 3rd power = 991,026,973.

The exponentiation form is mostly used to denote 997 cube.

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