Question

What is √2323 in simplest form as a radicand and a number outside the radicand

Answer 1

Since 2323 = 23*101 has no perfect square factors, this means we cannot simplify $\sqrt{2323$ into the form $a\sqrt{b}$

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 $\sqrt{232}$

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:

$\sqrt{232} = \sqrt{2^3*29}$

$\sqrt{232} = \sqrt{2^2*2*29}$

$\sqrt{232} = \sqrt{2^2*58}$

$\sqrt{232} = \sqrt{2^2}*\sqrt{58}$

$\sqrt{232} = 2*\sqrt{58}$

For the last two steps I used these square root rules

$\sqrt{x*y} = \sqrt{x}*\sqrt{y}$

$\sqrt{x^2} = x$ where x is nonnegative