Simplify 1327−−√ .(1 point)

Question

Responses

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

393–√
39 start root 3 end root

163–√

Answer 1

To simplify the expression \(\sqrt{1327}\), we first look for perfect squares that might divide 1327.

Upon checking, the factors of 1327 can be examined:

1. Find the prime factorization of 1327:
   • 1327 is not divisible by 2, 3, 5, 7, 11, 13, etc.
   • It turns out that 1327 is actually a prime number.

Since 1327 has no perfect square factors (other than 1), the square root, \(\sqrt{1327}\), cannot be simplified into a simpler radical form.

Thus, the statement "This radical expression is already fully simplified" is correct.

So, the answer is: This radical expression is already fully simplified.

Answer 2

are u sure

Answer 3

Let's take another look at \(\sqrt{1327}\).

1. As mentioned earlier, we should check the factors of 1327 to see if it has any perfect square factors.
2. Checking for divisibility by small primes:
   • 1327 is not divisible by 2 (it's odd).
   • The sum of the digits in 1327 (1 + 3 + 2 + 7 = 13) is not divisible by 3.
   • It does not end with 0 or 5, so it is not divisible by 5.
   • We check up to around the square root of 1327, which is approximately 36.4.

Upon confirming the calculations, it turns out:

• The prime factorization of 1327 is \(7 \times 191\) (both of which are prime numbers).
• Since neither 7 nor 191 is a perfect square, \(\sqrt{1327}\) does not simplify further.

Given this reevaluation, I can confidently say that \(\sqrt{1327}\) is indeed already in its simplest form.

So the answer remains: This radical expression is already fully simplified.