cube of any od number is even
Answers
Answer:
Q2) State true or false:
(i) Cube of any odd number is even.
(ii) A perfect cube does not end with two zeroes.
(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.
Solution:
(i) False
Since, 1^3=1,\ 3^3=27,\ 5^3=1251
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\ and\ 30^3=2700010
3
=1000, 20
3
=8000 and 30
3
=27000....so on.
(iii) False
Since, 5^2=25,\ 5^3=125,\ 15^2=225,\ 15^3=33755
2
=25, 5
3
=125, 15
2
=225, 15
3
=3375
(Did not end with 25)
(iv) False
Since 12^3=172812
3
=1728
Ends with 8
And 22^3=1064822
3
=10648
Ends with 8
(v) False
Since, 10^3=100010
3
=1000
Four digit number
11^3=133111
3
=1331
Four digit number
(vi) False
Since, 99^3=97029999
3
=970299
Six digit number
(vii) True
1^3=11
3
=1
Single digit number
2^3=82
3
=8
Single digit number