Simplify 13√27
1. 39√3
2. 39
3. This radical expression is already fully simplified
4. 16√3
The simplified form of 13√27 is 39√3. Therefore, the correct answer is 1.
To simplify the expression 13√27, we can break down 27 into its prime factors.
27 can be expressed as 3 * 3 * 3.
Simplifying 13√27, we can rewrite it as 13 * √(3 * 3 * 3).
Taking the square root of each factor inside the radical, we get 13 * 3√3.
Therefore, the simplified form of 13√27 is 39√3.
So, the correct answer is option 1: 39√3.
To simplify the expression 13√27, we need to find the prime factorization of 27.
The prime factorization of 27 is 3^3, since 3 × 3 × 3 = 27.
Now, let's simplify the expression:
13√27 = 13√(3^3)
Using the property of radicals, which states that √(a × b) = √a × √b, we can rewrite the expression as:
13 × √(3^3) = 13 × √3 × √(3^2)
Simplifying further, we have:
13 × 3 × √(3^2) = 39√3 × √(3^2)
Since √(3^2) = 3, we can simplify even more:
39√3 × √(3^2) = 39√3 × 3
Finally, multiplying the numbers, we get:
39 × 3 = 117
Therefore, the simplified expression of 13√27 is 117, which corresponds to option 2.