The smallest 5-digit integer perfect square is 10,000 = (100)2
The largest 5-digit integer perfect square is 99,856 = (316)2
So we want to know how many numbers that is, from 100 to 316 inclusive.
It's 316 minus the first 99 = 217 of them.
10 perfect squares
Two. 36, and 49 are perfect squares.
Eight of them.
There are twelve.
1 and 0. 12 = 1 02 = 0
900
500
5 of them.
There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).
Infinitely many, since every positive number is a square of some other number. However, there are 21 perfect squares (SQUARES OF INTEGERS). From 112 to 312, inclusive.
There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.There is no pair of perfect squares that sums to 21. And the question is pointless if it is not about perfect squares because in that case there are infinitely many answers.
683 perfect squares.
There are no four-digit perfect squares that are palindromes.
10 perfect squares
Two. 36, and 49 are perfect squares.
The concept of perfect squares has been known since ancient times, with early mathematicians from civilizations such as the Babylonians and Greeks recognizing them. However, it is difficult to attribute the discovery of the perfect squares sequence to a specific individual, as it evolved over centuries through various cultures. The sequence itself, defined as the squares of integers (1, 4, 9, 16, etc.), has been studied and utilized by many mathematicians throughout history.
sqrt(2000) = 44.7sqrt(20000) = 141.4So the perfect squares between 2000 and 20000 are the squares of 45 to 141 (inclusive)ie there are 97 perfect squares in the interval.