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(#M40002564) GATE question only one Keep an EYE

how many no.are b/w 1& 100 which are sqare and also cube?

Asked In Gate SOURABH VERMA (13 years ago)

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@SI-IW@NI 12U13EY  (13 years ago)

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

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Sandeep Thaker  (13 years ago)

1
64
Square of 1 is 1 and cube is also 1.
Square of 8 is 64 and cube of 4 is also 64.

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pankaj kumar  (13 years ago)

only one i.e 64

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kiran  (13 years ago)

ans=4,5^3=125>100

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pavan kumar  (13 years ago)

only 64 wich is the square of 8 and cube of 4

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Nirav Bhut  (13 years ago)

answer is 1

because only 64 is the number which is square and also cube.

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manish  (13 years ago)

we will consider

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Rakesh Kumar Kohli  (13 years ago)

Two numbers which are 1 and 64.
1 = 1*1 = 1*1*1
64 = 4*4*4 = 8*8

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jaspreet kaur  (12 years ago)

ans is 1 ie 64

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Indrani Mukherjee  (7 years ago)

1 and 64
1=1^2 and 1=1^3
64=8^2 and 64=4^3

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