You are told that 1331 is a perfect cube. Can you guess without factorization what is its cube root?
Similarly, guess the cube roots of 4913, 12167, 32768
Answers
By grouping the digits, we get 1 and 331
We know that, since, the unit digit of cube is 1, the unit digit of cube root is 1.
∴ We get 1 as unit digit of the cube root of 1331.
The cube of 1 matches with the number of second group.
∴ The ten's digit of our cube root is taken as the unit place of 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 \sqrt[3]{1331}=11∴31331=11
By grouping the digits, we get 4 and 913
We know that, since, the unit digit of cube is 3, the unit digit of cube root is 7.
∴ we get 7 as unit digit of the cube root of 4913.
We know 1^{3}=1 \text { and } 2^{3}=813=1 and 23=8 , 1 > 4 > 8.
Thus, 1 is taken as ten digit of cube root.
\therefore \sqrt[3]{4913}=17∴34913=17
By grouping the digits, we get 12 and 167.
We know that, since, the unit digit of cube is 7, the unit digit of cube root is 3.
∴ 3 is the unit digit of the cube root of 12167
We know 2^{3}=8 \text { and } 3^{3}=2723=8 and 33=27, 8 > 12 > 27.
Thus, 2 is taken as ten digit of cube root.
\therefore \sqrt[3]{12167}=23∴312167=23
By grouping the digits, we get 32 and 768.
We know that, since, the unit digit of cube is 8, the unit digit of cube root is 2.
∴ 2 is the unit digit of the cube root of 32768.
We know 3^{3}=27 \text { and } 4^{3}=6433=27 and 43=64, 27 > 32 > 64.
Thus, 3 is taken as ten digit of cube root.
\therefore \sqrt[3]{32768}=32∴332768=32
Answer:
Cube roots-
1331 - 11
4913- 17
12167- 23
32768- 32
Hope this helps u