Which of these integers cannot be expressed as the difference of two squares? 5 7 8 9 10
Question
Which of these integers cannot be expressed as the difference of two squares?
5
7
8
9
10
Solution
The integer that cannot be expressed as the difference of two squares is 8.
Here's why:
- 5 can be expressed as 3^2 - 2^2 = 9 - 4 = 5
- 7 can be expressed as 4^2 - 3^2 = 16 - 9 = 7
- 8 cannot be expressed as the difference of two squares. There are no two perfect squares that subtract to give 8.
- 9 can be expressed as 5^2 - 4^2 = 25 - 16 = 9
- 10 can be expressed as 6^2 - 4^2 = 36 - 26 = 10
So, the answer is 8.
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