Gate
Exam
how many no.are b/w 1& 100 which are sqare and also cube?
Read Solution (Total 10)
-
- 1 and 64...................since a number is a cube and square only when it is a square of a cubic no.
so here we all know about 1.
now we know that cubes of 2 digits no. is a 3 digit no. so we could check from 1to9.
and from 1 to 9 there exists only no.'s such as 1 and 8 which r cubes of a no.
viz. 2^3=8 n 1^3=1
so, 8^2=64 n 1^2=1
answers are 1 n 64
my trick in short: a no. is cubic as well as a perfect square only when it is the square of a cubic no. n cube of any 2 digit no. is a 3 digit no. so we searched the cubic no.'s from 1 to 9 - 13 years agoHelpfull: Yes(13) No(3)
- 1
64
Square of 1 is 1 and cube is also 1.
Square of 8 is 64 and cube of 4 is also 64. - 13 years agoHelpfull: Yes(4) No(2)
- only one i.e 64
- 13 years agoHelpfull: Yes(3) No(1)
- ans=4,5^3=125>100
- 12 years agoHelpfull: Yes(3) No(1)
- only 64 wich is the square of 8 and cube of 4
- 13 years agoHelpfull: Yes(1) No(1)
- answer is 1
because only 64 is the number which is square and also cube. - 12 years agoHelpfull: Yes(1) No(1)
- we will consider
- 13 years agoHelpfull: Yes(0) No(2)
- Two numbers which are 1 and 64.
1 = 1*1 = 1*1*1
64 = 4*4*4 = 8*8 - 13 years agoHelpfull: Yes(0) No(1)
- ans is 1 ie 64
- 11 years agoHelpfull: Yes(0) No(1)
- 1 and 64
1=1^2 and 1=1^3
64=8^2 and 64=4^3 - 7 years agoHelpfull: Yes(0) No(1)
Gate Other Question