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√(b)`

It seems like your teacher may have made a typo. I would double check with them.

-----------------------------------------------------------------------

I'll show you how to simplify a different problem. Let's say we want to simplify
`√(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:

`√(232) = √(2^3*29)`

`√(232) = √(2^2*2*29)`

`√(232) = √(2^2*58)`

`√(232) = √(2^2)*√(58)`

`√(232) = 2*√(58)`

For the last two steps I used these square root rules

`√(x*y) = √(x)*√(y)`

`√(x^2) = x` where x is nonnegative