Multiply and Divide Radicals Quick Check

Question

5 of 55 of 5 Items
Question
Simplify 1327−−√
.(1 point)
Responses

163–√
16 start root 3 end root

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

393–√
39 start root 3 end root

39

Answer 1

To simplify \( \sqrt{1327} \), we can start by factoring 1327 into prime factors.

1. First, we check if 1327 can be divided by smaller prime numbers (like 2, 3, 5, etc.) until we find factors.

   In this case, the number 1327 is actually equal to \( 39 \times 34 \).

2. Now, we can further factor \( 39 \) and \( 34 \):

   • \( 39 = 3 \times 13 \)
   • \( 34 = 2 \times 17 \)

   So, \( 1327 = 3 \times 13 \times 2 \times 17 \).

3. For square roots, we try to pair the factors. The expression has no perfect square factors, which means \( \sqrt{1327} \) cannot be simplified further.

Thus, the correct response is:

This radical expression is already fully simplified.