Squares and Cubes

Number Theory Level 1

1 is the 1st positive integer that is both a perfect square and a perfect cube. What is the 2nd positive integer that is both a perfect square and a perfect cube??


The answer is 64.

Romel Campos by Romel Campos , 29, Philippines

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5 solutions

Romel Campos
Mar 31, 2014

the first number that has perfect square and cube is 1 then we need to find the 2nd (2)^2)^3=(2)^3)^2 4^3=8^2 64=64

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Isabella Amabel
Apr 20, 2014

We should look for a number which is the 6th power of a number. Thus, since the number is 2nd, 2^6 =64

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Gian Alix
Apr 1, 2014

It's like saying that 1 is the first number which is a perfect sixth power, and that the problem asks for the next number which is a perfect sixth power, which is 64.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

The power has to be divisible by both 2 and 3.

Thus 2^6 = 64 is the answer.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Vishnudatt Gupta
May 2, 2014

in this question we should try the next natural numbers sixth power

i.e 2 2 2 2 2*2=64

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You mean 2 2 2 2 2*2.

Kamala Ramakrishnan - 6 years, 11 months ago

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