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What is the value of the cube root $− 512 729 3$ ?

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− 7 9

− 8 9

79

89

answer is B.

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Detailed Solution

The given cube root is

− 512 729 3 .

To find the cube of any number, first, find the factorization of that number, then group all the factors in triplet form.
Find the prime factorization of 512 and 729.

2 512 2 256 2 128 2642322162824221

3729324338132739331

Prime factorization of 512 and 729 are given as:

We have:

Now,

Therefore, the value of the cube root

− 8 9 .

Hence, option (2) is correct.

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