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Question

Can you guess the cube roots of the following without factorization?

(iii)32768


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Solution

Find the cube root using estimation

To guess the cube root of 32768, this number has to be separated into groups of three starting from the rightmost digit.
The groups are 32 and 768.
When we consider the group 768,
since 768 ends with 8 and we know that if the digit 8 is at the end of any perfect cube number, then its cube root will have 2 at its unit place only. Therefore, the digit at the unit place of the required cube root will be 2.

When we consider the group 32,
We know that 33=27 and 43=64
Also, 27<32<64
So, 3 will be taken at the tens place.

Hence, the cube root of 32768 is 32.


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