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]