Question

5) T.U marks
How many positive numbers less that 50000 exist which are both perfect squares and perfect cubes?​

Answer 1

Given :   positive numbers less than 50000

To Find :  how many positive numbers less than 50000  exist which are both perfect squares and perfect cubes​

Solution:

a²    =  b³

so b must be  square number

So that

( a³)² = ( a²)³

=> a⁶  

Let check

1   1

2   64

3   729

4    4096

5   15625

6   46656

______________

7   117649

so there are 6 positive numbers less than 50000 exist which are both perfect squares and perfect cubes​

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