Q.3 You are told that 1,331 is a perfect cube. Can you guess without factorisation what
is its cube root? Similarly, guess the cube roots of

4913,

12167,

32768.

Answers (1)

We have 1331.

Divide number in two parts:   First part is 1 and second is 331.

  Since the given number is ending with 1 so the last digit of cube root will be 1.

In the first part, we have 1.

So  1^3 = 1

By estimation, the cube root of 1331 is 11.

Similarly for all other parts.

4913:-    First part is 4 and the second part is 913.

              The number is ending with 3 so its cube root will have 7 at units place.

              In the first part, the nearest cube root is 1.

               So cube root of 4913 is 17.

12167:-    First part is 12 and the second part is 167.

                The number is ending with 7 so its cube root will have 3 at units place.

                 In the first part, the nearest cube root is 2.

               So cube root of 12167 is 23.

32768:-   First part is 32 and the second part is 768.

                The number is ending with 8, so its cube root will have 2 at units place.

                In the first part,  nearest cube root is  3.

                So cube root of 32768 is 32.

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