Question

By prime factorisation find wheather the following are perfect cubes.
9702​

Answer 1

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The cubed root of nine thousand, seven hundred and two ∛9702 = 21.328178007758

Process :

The process of cubing is similar to squaring, only that the number is multiplied three times instead of two. The exponent used for cubes is 3, which is also denoted by the superscript³. Examples are 4³ = 4*4*4 = 64 or 8³ = 8*8*8 = 512.

The cubic function is a one-to-one function. Why is this so? This is because cubing a negative number results in an answer different to that of cubing it's positive counterpart. This is because when three negative numbers are multiplied together, two of the negatives are cancelled but one remains, so the result is also negative. 7³ = 7*7*7 = 343 and (-7)³ = (-7)*(-7)*(-7) = -343. In the same way as a perfect square, a perfect cube or cube number is an integer that results from cubing another integer. 343 and -343 are examples of perfect cubes.

Answer 2

Answer:

As we can see 2*3²*7²*11

here the cube is not possible as √9702=

98.498731

and it isn't a perfect cube

hope it helps you