Find the ones digit of the cube of 141. State the value also.
Answers
Answer:
141 cubed, (141)3, is the number you get when multiplying 141 times 141 times 141.
It can also be looked at as exponentiation involving the base 141 and the exponent 3.
The term is usually pronounced 3rd power of one hundred forty-one or one hundred forty-one cubed.
The cube of 141 is a perfect cube because the number is the product of the three equal integers 141.
It can be written as 141 × 141 × 141 or in exponential form.
Read on to learn everything about the number one hundred forty-one cubed, including useful identities.
The inverse operation of cubing 141 is extracting the cube root of 141, explained here.
In the next section we elaborate on the cube 141.
What is 141 Cubed?
A cube is a three-dimensional shape with 6 equal square faces.
Hence, a cube with side length 141 has an area of 2,803,221.
The sum and the differences of two cubes, for example with side length 141 and 140, can be calculated with the following formulas:
a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 141, b = 140 and the equivalence we get:
(141)3 = 281 x (1412 – 141 × 140 + 1402) – 1403 = 281 x (19881 – 19740 + 19600) – 2744000 = 281 x 19741 – 2744000 = 2,803,221
a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 141, b = 140 and the equivalence we get:
(141)3 = (1412 + 141 × 140 + 1402) + 1403 = 19881 + 19740 + 19600 + 2744000 = 2,803,221
As follows from (1), 141 cubed can be calculated from 140 cubed and 141 squared using the identity:
n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
(141)3 = (2 × 141 – 1) × (1412 – 141 + 1) – (140)3 = 281 × (19881 – 140) – 2744000 = 281 × 19741 – 2744000 = 2,803,221
Using the second formula 141 cubed can be also be computed with this identity:
n3 = (n-1)3 + 3n2 -3n + 1
(141)3 = 1403 + 3 × 1412 – 3 × 141 + 1 = 2744000 + 3 × 19881 – 3 × 141 + 1 = 2744000 + 59643 – 423 + 1 = 2,803,221
If you want to calculate the cube of any number, not only integers like 141, you can use our calculator above.
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A cube similar to 141 is, for example: cube of 143.