How many perfect squares are there in the below set? [1^1, 2^2, 3^3, 4

There is a strict to calculate the square of numbers ending with 5

I did 45^2 = [4*(4+1)](25) = 2025

2017 is close and little less than 2025 i.e. √2017 ≈ 44.5

i.e. squares from 1 to 2017 will be 44 (1^2 to 44^2)

I hope this helps!!!
Mo2men

Apatel91

Answering to your PM

A perfect square is a number which has even exponents of all it's prime factors

So the first case is the numbers whose exponents are even e,g, 2^2, 4^4, 6^6, 8^8 etc.
We have 2017 numbers i.e. their powers also are from 1 to 2017 so the even exponents cases will be the count of even numbers from 1 to 2017 i.e. 1008


Now, there may be some number which are such as 9^9 these numbers are perfect squares because their base (9) itself is a perfect square.
Such numbers = all perfect squares from 1 to 2017 which is 44

But there may be several common numbers such as 4^4, 16^16 which have been considered in the previous two cases so we need to exclude them
These numbers will be even perfect square to the power even
From 1 to 2017, we have 44 perfect squares and 22 of them are even so we subtracted these 22 cases

I hope this helps now!!!

Total Numbers of type 1= even^even= {2,4,6...2016}=1008
Include 1= we have 1009
Now include any (n^2)^anything= would be >1

Hence ans has to be more than 1009

E)