Question

which of the following are perfect cubes? 1)243 2)400 3)500 4)512 5)729. with the solution method .give reasons

Answer 1

HEY MATE HERE IS YOUR ANSWER


The perfect cubes are 243

By Multiply 7 three times we get 243

So therefore 243 is a perfect cube.

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Hope it will help you

Answer 2

First prime factorize all the numbers :

243 = $3^{5}$

400 = $2^{4} * 5^{2}$

500 = $5^{3}* 2^{2}$

512 = $2^{9}$

729 = $3^{6}$

If a number has to be a perfect cube, the powers of the number has to divisible  by 3.

In this case only 512 and 729 and perfect cubes.