Answer:
2√2 -√6
Explanation:
You want to know the surd representation of the irrational number that rounds to 0.378937382.
Trial and error
The plural "surds" suggests this is the difference of two irrational roots. Looking at √(n+1) -√n, we find that √3 -√2 is the nearest, but does not match.
Looking at √(n+2) -√n, we find that √8 -√6 matches all 9 digits when rounded to the 9th decimal place. 20 digits of that value are ...
0.37893738196301199941
The given number approximately matches the irrational value ...
2√2 -√6
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Additional comment
We programmed a calculator to find the values of √(n+2) -√n for n = 1..10. The result is attached. The 6th value matches, and corresponds to n=6.
In general, finding a surd representation of an arbitrary value seems to be a matter of trial and error. Perhaps your curriculum materials offer an algorithm.