This is a beautiful problem from ISI MSTAT 2019 PSA problem 11 based on multiplication principles. We provide sequential hints so that you can try.
How many positive divisors of 
are perfect squares?
Basic counting principles
Divisors of a number
Answer: is 18
ISI MStat 2019 PSA Problem 11
A First Course in Probability by Sheldon Ross
See in order to get the positive divisors of that are perfect squares , we need to take only the even powers of the primes {2,5,11}.
Now the maximum powers of 2 is 5 . So there are 3 choices for even powers {0,2,4} .
The maximum powers of 5 is 3 . So there are 2 choices for even powers {0,2}.
Now the maximum powers of 2 is 5 . So there are 3 choices for even powers {0,2,4} .
The maximum powers of 11 is 4 . So there are 3 choices for even powers {0,2,4}.
Hence by multiplication principle we have in total 
such positive divisors.
This is a beautiful problem from ISI MSTAT 2019 PSA problem 11 based on multiplication principles. We provide sequential hints so that you can try.
How many positive divisors of are perfect squares?
Basic counting principles
Divisors of a number
Answer: is 18
ISI MStat 2019 PSA Problem 11
A First Course in Probability by Sheldon Ross
See in order to get the positive divisors of that are perfect squares , we need to take only the even powers of the primes {2,5,11}.
Now the maximum powers of 2 is 5 . So there are 3 choices for even powers {0,2,4} .
The maximum powers of 5 is 3 . So there are 2 choices for even powers {0,2}.
Now the maximum powers of 2 is 5 . So there are 3 choices for even powers {0,2,4} .
The maximum powers of 11 is 4 . So there are 3 choices for even powers {0,2,4}.
Hence by multiplication principle we have in total such positive divisors.
