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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 32768.

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   32768.

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years 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 32 and 768.

Since, the unit digit of the cube is 8, the unit digit of the cube root is 2.

Therefore, 2 is the unit digit of the cube root of 32768.

We know 33 = 27 and 43 = 64 , 27 > 32 > 64.

Thus, 3 is taken as ten-digit of the cube root.

∛32768= 32

Thanks

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