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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 12167

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   12167 

Grade:12

1 Answers

Anand Kumar Pandey
askIITians Faculty 5653 Points
5 months ago
Dear Student

By grouping the digits, we get 1 and 331

Since, the unit digit of cube is 1, the unit digit of cube root is 1.

Therefore, we get 1 as the unit digit of the cube root of 1331.

The cube of 1 matches with the number of the second groups.

Therefore, the ten’s digit of our cube root is taken as the unit place of the smallest number.

We know that the unit’s digit of the cube of a number having digit as unit’s place 1 is 1.

∛1331 = 11


By grouping the digits, we get 12 and 167.

Since the unit digit of the cube is 7, the unit digit of the cube root is 3.

Therefore, 3 is the unit digit of the cube root of 12167

We know 23 = 8 and 33 = 27, 8 > 12 > 27.

Thus, 2 is taken as the tenth digit of the cube root.

∛12167= 23

Thanks

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