Question

you are told that 1331 is a perfect cube can you guess without factorization what is its cube root? similarly guess the cube root of 4913 ,12167, 32768

Answer 1

Solution:

We know that 10³ = 1000 and Possible cube = 11³ = 1331 Since, cube of units digit 1³ = 1.

Therefore, cube root of 1331 is 11.

4913 :--

We know that 7³ = 343

Nealy number comes with 7 as unit place 17³ = 4913. Hence, cube of 4913 is 17.

12167 :--

We know that 3² = 27

Hence, next number comes with 7 as centre place = 17³ = 2167 and next number with 3 as one's digit 23³ = 12167, Hence cube root of 121667 is 23.

32768 :--

We know that 2³ = 8

Here in cube, one's digit = 8

Now, next number with 2 as one's digit 12³ = 1728

and next number with 2 as one's digit 22³ = 10648 and next number with as one's digit 32³ = 32768.

Therefore, 32768 is 32 cube root.