Simplify 1327−−√

Question

.(1 point)
Responses

393–√
39 start root 3 end root

163–√
16 start root 3 end root

This radical expression is already fully simplified.
This radical expression is already fully simplified.

39

Answer 1

To simplify \( \sqrt{1327} \), we can start by checking if it can be expressed in terms of simpler radicals or integers.

We can factor 1327 to see if it has any perfect square factors:

1. Start by dividing 1327 by small prime numbers:
   • It is not even, so 2 doesn't work.
   • The sum of the digits (1 + 3 + 2 + 7 = 13) is not divisible by 3.
   • It doesn't end with 0 or 5, so it's not divisible by 5.

Continuing to check other prime numbers leads us to find that 1327 is actually a prime number.

Since 1327 does not have any perfect square factors, the expression \( \sqrt{1327} \) is already fully simplified.

Thus, the correct response is: This radical expression is already fully simplified.