Since 2323 = 23*101 has no perfect square factors, this means we cannot simplify [tex]\sqrt{2323[/tex] into the form [tex]a\sqrt{b}[/tex]
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 [tex]\sqrt{232}[/tex]
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:
[tex]\sqrt{232} = \sqrt{2^3*29}[/tex]
[tex]\sqrt{232} = \sqrt{2^2*2*29}[/tex]
[tex]\sqrt{232} = \sqrt{2^2*58}[/tex]
[tex]\sqrt{232} = \sqrt{2^2}*\sqrt{58}[/tex]
[tex]\sqrt{232} = 2*\sqrt{58}[/tex]
For the last two steps I used these square root rules
[tex]\sqrt{x*y} = \sqrt{x}*\sqrt{y}[/tex]
[tex]\sqrt{x^2} = x[/tex] where x is nonnegative
