Question

State true or false.
(i) Cube of any odd number is even.

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

(iii) If 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 1

(i) Cube of any odd number is even.

FALSE: Odd multiplied by odd is always odd

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

TRUE: A perfect cube will end with odd number of zeroes

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

TRUE: $5$ multiplied by $5$ any number of times always gives $5$ at units place

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

False: $2^3=8$

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

FALSE: The smallest two digit number is $10$ and ${10}^3$ $=1000$ is a three digit number

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

FALSE: $99$ is the largest $2$ digit number; ${99}^3$ $=989901$ is a $6$ digit number

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

TRUE: $2^3=8$ is a single digit number.