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2.State True or False.
(i) Cube of an odd number is even.

(ii) A perfect cube does not end with two zeros.

(iii) If the square of a number ends with 5, then its cube ends with 25.

(iv) There is no perfect cube which ends with 8.

(v) The cube of a two digit number may be a three digit number.

(vi) The cube of a two digit number may have seven or more digits.

(vii) The cube of a single digit number may be a single digit number.


Answer :

(i) False because Cube of any odd number is always odd, e.g., \((3)^3 = 27\)

(ii) True.

(iii) True. For e.g., \((5)^2 = 25\) and \((5)^3 = 625\)

(iv) False because there exists perfect cube which ends with 8 for e.g., \((12)^3 = 1728 \)ending with 8

(v) False. let's take the lowest two digit number i.e., \((10)^3 = 1000\)which is a 4-digit number.

(vi) False.Let's take the highest two digit number i.e., \((99)^3 = 970299 \) which is 6-digit number.

(vii) True. For e.g., \((2)^3 = 8\) which is 1-digit number.