Since 2323 = 23*101 has no perfect square factors, this means we cannot simplify
into the form

It seems like your teacher may have made a typo. I would double check with them.
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I'll show you how to simplify a different problem. Let's say we want to simplify

Find the prime factorization of the radicand:
232 = 2^3*29
we can rewrite the "2^3" as "2^2*2" to pull out the perfect square factor, which helps us simplify as such:





For the last two steps I used these square root rules

where x is nonnegative