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Q.

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


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a

−7 9

b

−8 9

c

7 9

d

8 9  

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 2 64 2 32 2 16 2 8 2 4 2 2 1               3 729 3 243 3 81 3 27 3 9 3 3 1
Prime factorization of 512 and 729 are given as:  Question Image We have:  Question Image Now,  Question ImageTherefore, the value of the cube root Question Imageis −8 9 .
Hence, option (2) is correct.
 
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