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3/4 plywood over a 3' span is likely to be fine as long as she does not sit or climb up on it, or leave heavy objects near the edge for long periods of time.
I am sitting at a desk, as i right this that is 3/4 plywood spanning 6' and it is fine. If i put a straight edge on it i think i may see a sag of about an 1/8", with out my heavy arms resting on ...
1
Use the Sagulator to find out. I entered your dimensions, assumed a load of 30 lbs distributed over the top, and said you're using 3/4" fir plywood. The total calculated sag was 0.01", which seems quite acceptable.
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