Simplify 13sqrt(27) (1 point)
O 16sqrt(3)
O 39sqrt(3)
This radical expression is already fully simplified.
39
sqrt(3)
To simplify the expression 13√(27), we start by simplifying the square root. The square root of 27 can be simplified as follows:
√(27) = √(9 × 3) = √9 × √3 = 3√3
Therefore, the expression 13√(27) simplifies to 13 * 3√3.
Multiplying 13 and 3 gives us:
13 * 3√3 = 39√3
So, the simplified expression is 39√3. The correct option is O 39√3.
To simplify the expression 13√27, we need to find the prime factorization of 27.
Start by dividing 27 by the smallest prime number, which is 3:
27 ÷ 3 = 9
Next, divide 9 by 3:
9 ÷ 3 = 3
Now, we have the prime factorization of 27, which is:
27 = 3 × 3 × 3
Since the square root of 9 is 3, we can rewrite √27 as:
√27 = √(3 × 3 × 3)
Pull out any pairs of identical numbers from under the square root:
√27 = 3√3
Finally, simplifying the expression 13√27:
13√27 = 13 × 3√3
Multiplying the coefficients:
13 × 3 = 39
Therefore, 13√27 simplifies to 39√3. So, the correct answer is O 39√3.