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Q.

The cube root of 238328 is:


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a

  52

b

  62

c

  72

d

  82

answer is B.

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Detailed Solution

      Concept: In cube root generally, we use prime factorization method for small numbers but since the number mentioned in theQuestion statement is large, to solve this question, we will use estimation method to obtain our desired answer. In the execution of the estimation method, we will break down our concerned number in two equal number of its digits, i.e., for example, say if the number is a 3-digit number, we will consider the first 3 digits from the left as a group and the last 3 digits as another group.
Then, we will find out the digits of whose, either both of the groups are exact cubes or we will consider the smaller digit between the two of whose cubes, lie our concerned group (number) . We will combine the digits according to the order of the respective groups, i.e., which one to be on the right and which one to be on the left, and we will obtain our required answer.
Given, number is 238328.
Now, 238328 is an even number, so its cube root has to be an even number.
Let us make 2 groups, 238 and 328, grouping the first three digits from the right in one, and the last three digits in another. Therefore, the first Group consists of 328 whose unit digit is 8. So, unit digit of cube will be 2 since https://lh6.googleusercontent.com/JGaNyG7r9eWh2pzeIpBKYPBXqVyodU1lo4_lL7iB3Mnz88x-uRU_e0DkvRKZTdCgv9FiOA7Wk_ODJzct4M2xnvMgNSzGnYGBoHlYbfkdUJe99xrRMRXD05RhPYWXbhn_JaX5ZWNPEGwKGDp7T43aJg.
And second Group is 238, i.e.,
it lies between cube of 6 https://lh3.googleusercontent.com/reiSXixszcIrOH7K2ISZqBZp_7_FTeYs_0hkVBsgZ-c56bipwqp2dy82pfnfvpkhis2acJLzihqEDryxLPzmGXWzRMVgYxIKhpWkfhQefbeNaXxz2Nel2ozLLLjTi3vh6VYGy5bvoYS2jH_xn3xrRg and cube of 7 https://lh6.googleusercontent.com/B7vFdkS4qyRaGC81VW-5WBKaBSH1kOubA0DRSrkRYe1Czwy8OtybVHUZwwpB3hAzDiAjybfc-liNWTiX04QMwNRs_BsvsIpvUn2fmKuZeHDBcGXKmdh6croawk-G8Kr-9F4ORhnQ4YiuA_fV_DmujA.
Thus, taking the smaller number “6” as tens place, we get the cube root of 238328 = 62.
Hence, the Correct Answer is 2) 62.
 
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