Question
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
Upstudy AI Solution
Tutor-Verified Answer
Answer
You can fill the blank with either 4 or 9 to make the expression evaluate to a perfect square.
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If
: -
If
:
Final Answer:
The blank can be filled with 4 or 9.
Solution

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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?