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10 perfect squares

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Q: How many perfect squares exist between one and one hundred?
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How many perfect squares exist between one million and one billion?

30,622


What is the number of perfect squares that exist in base 5 system?

There are infinitely many, just like in base 10. In any base system, the number of perfect squares is the same. Take the natural (counting) numbers 1, 2, 3, .... Squaring each of these produces the perfect squares. As there are an infinite number of natural numbers, there are an infinite number of perfect squares. The first 10 perfect squares in base 5 are: 15, 45, 145, 315, 1005, 1215, 1445, 2245, 3115, 4005, ...


When 96 is added to a perfect square another perfect square is obtained How many such pairs of perfect squares exist?

96 + 4 = 100 96 + 25 = 121 96 + 100 = 196 96 + 529 = 625


Does perfect competition exist?

No, Perfect Competition is just an imaginary one and it does not exist at all.


Weighted Least Squares regression?

Yes, it does exist.


How many perfect squares exist between one hundred thousand and one million?

I make it 684. Would you like a list? The first time I wrote a program to compare the square root of each number from one hundred thousand to one million, and counted only those that were whole. It was late at night, and by compiling my code this brute force approach cranked out an answer in under 30 seconds. Maybe less, I don't remember. I started to rewrite the same program just now, as I see there has been more activity on this question, but then I realized what a mental midget I had been. In thinking about code optimization it occurred to me that the square root of one million is one thousand, and so to count the perfect squares all I need to do was subtract the integral value of the square root of one hundred thousand (316) from 1000. Each of those numbers has a perfect square in the given range. 1000-316 = 684. Had I bothered to produce a list of numbers from the original program I would have immediately realized my foolishness.


What is the smallest negative perfect square that is divisible by the four smallest prime numbers?

Perfect squares are positive. A smallest negative number doesn't exist. The four smallest prime numbers are 2, 3, 5 and 7. The smallest perfect square would have to be 2^2 x 3^2 x 5^2 x 7^2 or 44,100


What is the present perfect tense of exist?

The present perfect tense is has/have existed.


Does a perfect cube exist?

only in art


What is the PERFECT food cost?

Perfect food cost does not exist. This is different depending on the business and its financial structure.


Does perfect competition market exist in the market world?

Check


What is the past tense and past perfect tense of exist?

Existed is the past tense. The past perfect tense is had existed.