the integer 49 can be written as the sum of smaller perfect squares in a variety of ways. one such way includes six terms: 25+9+4+1+1. if each term has a value between 0 and 49,what is the fewest number of perfect square terms that can be added together for a sum of 49?
Toon Link copied word for word from my website!(Brain.ly)
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the person in the brain.ly also cheated, that's aops's answer bruh
Well, it seems like you're trying to make 49 out of perfect squares and want to use the fewest number of terms possible. Let me put on my clown wig and give you a funny answer!
To find the fewest number of perfect square terms that add up to 49, you should call it "Squarantine" because we're keeping those squares at a safe distance!
Now, let's see if we can solve this puzzle. Since we want to use the fewest number of terms, we'll try to maximize the value of each term. The largest perfect square that is less than or equal to 49 is 49 itself (which means there's no need to take the square root of that pun!). So, we'll start with 49.
49 itself is a perfect square, and there you have it, we reached 49 using only one term! Mission accomplished, right? I hope this little mathematical clowning around brings a smile to your face!
To find the fewest number of perfect square terms that can be added together for a sum of 49, we can start with the largest perfect square less than or equal to 49, which is 49 itself.
Subtracting 49 from 49 leaves us with 0, so we have our first term, 49.
Now, let's find the largest perfect square less than or equal to the remaining number, 0. The largest perfect square less than 0 is 0 itself.
Subtracting 0 from 0, we have our second term, 0.
Since we have reached 0, we can stop because any further perfect square terms would be redundant.
Therefore, the fewest number of perfect square terms that can be added together for a sum of 49 is 2 (49 + 0).
First, we would like to determine if 49 can be written as the sum of two perfect squares.
49 - 1 = 48, which is not a perfect square.
49 - 4 = 45, which is not a perfect square.
49 - 9 = 40, which is not a perfect square.
49 - 16 = 33, which is not a perfect square.
49 - 25 = 24, which is not a perfect square.
We don't need to check any other squares, as 25 > 49/2.
Now, we check to see if there are three perfect squares that sum to 49. With a little work, we see that 49 = 4 + 9 + 36. Thus, the fewest number of perfect square terms that can be added together to sum to 49 is 3.
hope dis halps!
may Nayru guide you! :) (U probably don't know wut I'm talking about.)