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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.

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)
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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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