Question

write the cubes of five natural numbers of which are multiple of 7 and verify the following. The cube of a multiple of 7 is a multiple of 7 cube

Answer 1

Five multiples of 7 can be written by choosing different values of a natural number n in the expression 7n.
Let the five multiples be 7, 14, 21, 28 and 35.
The cubes of these numbers are: 7 = 343, 14 = 2744, 21 = 9261, 28 = 21952, and 35 = 42875
Now, write the above cubes as a multiple of 7 . Proceed as follows:
343 = 7 x l
2744 = 14 = 14 x 14 x 14 = (7 x 2) x (7 x 2) x (7 x 2) = (7 x7 x 7) x (2 x 2 x 2) = 7 x 2
9261 = 21 = 21 x 21 x 21 = (7 x 3) x (7 x 3) x (7 x 3) = 7 x 3
21952 = 28 = 28 x 28 x 28 = (7 x 4) x (7 x 4) x (7 x 4) = (7 x 7 x 7) x (4 x 4 x 4) =7 x 4
42875 = 35 = 35 x 35 x 35 = (7 x 5) x (7 x 5) x (7 x 5) = (7 x 7 x 7) x (5 x 5 x 5) = 7 x 5
Hence, the cube of multiple of 7 is a multiple of 7 .

Answer 2

Answer:

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