How to determine the number of perfect squares between from 1 to 10000?

Each whole number from 1 to 100 gives a perfect square number in that interval when you square it. So there are obviously 100 of them.

100

1² = 1 (from 1 to 1 there is 1 perfect square)

2² = 4 (from 1 to 4 there are 2 perfect squares)

3² = 9 (from 1 to 9 there are 3 perfect squares)

...

100² = 10,000 (from 1 to 10,000 there are 100 perfect squares).

Answer:

Because √10,000 = 100, there are 100 perfect squares from 1 to 10,000.

1^2 ...2^2 ....3^2 ......n^2

n^2 = 10,000

so

n = √10,000 = 100

√10000 = 100 <-- Answer

ie every number from 1 to 100 can be squared to make a perfect square in the range 1 to 10000

Find the highest perfect square which is less 10000 first

sqrt(10000) = 100

so perfect square for 1 to 100 ( 100 numbers are perfect squares)

1*1, 2*2, through ... 100*100