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
Answer:
Step-by-step explanation:
Similarly, guess the cube roots of 4913, 12167, 32768. 1331=we divide 1331 into groups of three digits starting from the right. So 1331 has two groups one is 331 and another is 1. ... So one's place of the required cube root is 7
Solution:
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.
Therefore, ∛1331 = 11
By grouping the digits, we get 4 and 913
We know that, since the unit digit of the cube is 3, the unit digit of the cube root is 7.
Therefore, we get 7 as unit digit of the cube root of 4913.
We know 13 = 1 and 23 = 8 , 1 > 4 > 8.
Thus, 1 is taken as ten-digit of the cube root. Therefore, ∛4913 = 17
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.
Therefore, ∛12167= 23
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.
Therefore, ∛32768= 32