How many perfect squares less than 1000 end with the digit 5?
they will be of the form (5n)^2 where n is odd, so n = 2k+1
That makes them of the form (10k+5)^2 where 10k+5 < √1000
so now we have
10k+5 < 31
10k < 36
k < 3
So the only perfect squares less than 1000 and ending in 5 are
5^2 = 25
15^2 = 225
25^2 = 625
Well, I don't want to be too square, but let me think about this. So, the perfect squares less than 1000, include numbers like 1, 4, 9, 16, and so on. Now, if we're only looking for ones that end in 5, we can skip right past those numbers in between, like 11, 14, or 19. Finally, we get to 25, which has a 5 at the end. So, that's one square. And if we keep going, we'll find another one: 225. So, to answer your question, there are just two perfect squares less than 1000 that end with the digit 5. You could say they really "squarely" made it into that category!
Btw i changed my name but idk i think its division or subtraction idk
To find the number of perfect squares less than 1000 that end with the digit 5, we can analyze the pattern of perfect squares.
1) First, we know that for a perfect square to end with the digit 5, its units digit must be either 5 or 0. Since we are looking for perfect squares less than 1000, the 10's digit of the perfect squares can be any digit from 0 to 9.
2) We can start by identifying the perfect squares whose 10's digit is 0. The perfect squares with 10's digit 0 that end with the digit 5 are 25, 225, and 625.
3) Next, we can look at the perfect squares with 10's digit 1 to 9. To find these, we need to consider the possible values of the units digit that will result in a perfect square ending with 5.
- For the units digit 5, the possible numbers are 15, 35, 55, 75, 95 (since 15^2 = 225, 35^2 = 1225, 55^2 = 3025, 75^2 = 5625, 95^2 = 9025). But we are only interested in numbers less than 1000, so 75 and 95 are not relevant.
- For the units digit 0, the possible numbers are 10, 20, 30, 40, 60, 70, 80, 90 (for example, 10^2 = 100, 20^2 = 400, 30^2 = 900).
4) Putting it all together, the perfect squares less than 1000 that end with the digit 5 are: 25, 225, 625, 1225, 3025 (5 in total).
Therefore, there are 5 perfect squares less than 1000 that end with the digit 5.