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.
(i) Separating the given number (1331) into two groups :
1331 1 and 331
∵ 331 end in 1
∴ Unit's digit of the cube root = 1
∵ 13 = 1 and
∴ Ten's digit of the cube root = 1
∴
(ii) Separating the given number (4913) in two groups:
4913 4 and 913
Unit's digit:
∵ Unit's digit in 913 is 3
∴ Unit's digit of the cube root = 7
[73 = 343 : which ends in 3]
Ten's digit:
∵ 13 = 1, 23 = 8
and 1 < 4 < 8
i.e. 13 < 4 < 23
∴ Then ten's digit of the cube root is 1.
∴
(iii) Separatibng 12167 in two groups:
1216712 and 167
Unit's digit :
∵ 167 is ending in 7 and cube of a number ending in 3 ends in 7
∴ The unit's digit of the cube root = 3
Ten's digit
∵ 23 = 8 adn 33 = 27
Also, 8 < 12 < 27
or, 23 < 12 < 32
∴ The tens digit of the cube root can be 2.
Thus,
(iv) separating 32768 in two groups:
32768 32 and 786
Unit's digit:
768 will guess the unit's digit in the cube root.
∵ 768 ends in 8.
∴ Unit's digit in the cube root = 2
Ten's digit:
∵ 33 = 27 and 43 - 64
Also, 27 < 32 < 64
or, 33 < 32 < 43
∴ The ten's digit of the cube root = 3
Thus,