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) False

Since, $1^3=1,3^3=27,5^3=125,....$are all odd.

(ii) True

Since, a perfect cube ends with three zeroes.

e.g. $10^3=1000,20^3=8000,30^3=27000,....$so on

**(iii) False **

Since, $5^2=25,5^3=125,15^2=225,15^3=3375$

(Did not end with 25)

**(iv) False **

Since $12^3$ = 1728

[Ends with 8]

And $22^3$= 10648

[Ends with 8]

**(v) False **

Since = 1000

[Four digit number]

And $11^3$ = 1331

[Four digit number]

(vi) False

Since $99^3$= 970299

[Six digit number]

**(vii) False **

$1^3=1$

[Single digit number]

$2^3= 8$

[Single digit number]