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OPEN MIDDLE - Perfect Squares Slrections: Using the digits 1-9, at most one time each, to fill expression evaluate to a perfect square number.

Ask by Hobbs Stewart. in the United States
Jan 24,2025

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Answer

You can fill the blank with either 4 or 9 to make the expression evaluate to a perfect square.
  • If :
  • If :
Final Answer:
The blank can be filled with 4 or 9.

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Mind Expander

To solve the expression such that it evaluates to a perfect square using the digits 1-9 only once, let’s first simplify the expression to . This means we need to equal a perfect square.
Since , we need to be such that for some integer . Hence, must also contain factors that contribute to the squarity. We can try various numbers from 1-9 to see if the product with 36 yields a perfect square.
Here’s a fun check: if we pick , we get , which is , a perfect square! Using that logic, our digits used are 1, 2, and 8 (for 18).
So, one suitable solution could be filling in the blanks as :
Now you have a perfect square! Keep exploring with other digits to find different combinations; who doesn’t love a good perfect square hunt?

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