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

Which method should I use ?​

Answer 1

Step-by-step explanation:

You are told that 1,331 is a perfect cube. Can you guess without factorization what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.

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1331:

It lies between 10³ = 1000 and 20³ = 8000 and it’s last digit, 1, can’t be the cube but of 1, so:

Third root of 1331 = 11

4913:

It lies between 10³ = 1000 and 20³ = 8000 and it’s last digit, 3, can’t be the last digit of the cube of but 7, so:

Third root of 4913 = 17

12167:

It lies between 20³ = 8000 and 30³ = 27000 and it’s last digit, 7, can’t be the last digit of the cube of but 3, so:

Third root of 12167 = 23

32768:

You could proceed as above, but if you have had any contact with ‘bytes’, ‘kilobytes’, ‘megabytes’, you will have learned by heart that

32768 = 1024 * 32 = 2^10 * 2^5 = 2^15, so:

Third root of 2^15 = 2^5 = 32.

Cheers.