Simplify 13√27.
We can simplify this expression by converting the number inside the square root to its simplest radical form.
First, we can break down 27 into its prime factors:
27 = 3 * 3 * 3 = 3^3
Now, we can rewrite the expression as:
13√(3^3)
Since we have a cube root, we can simplify the expression by taking out one factor of 3 from inside the square root:
13 * 3√3
So, the simplified form of 13√27 is 13 * 3√3
To simplify the expression 13√27, we need to find the largest perfect square that divides evenly into 27.
The prime factorization of 27 is 3 x 3 x 3.
Since there are three 3's, we can take out one of them as a perfect square. This leaves us with 3 x 3 = 9.
So, 27 can be written as 9 x 3.
Now we can simplify the expression 13√27 as 13√(9 x 3).
Using the property of radicals, we can split the square root of a product into the product of square roots.
13√(9 x 3) = 13√9 x √3.
The square root of 9 is 3, so we can simplify further:
13√9 x √3 = 13 x 3√3.
Therefore, the simplified expression 13√27 is equal to 39√3.
To simplify 13√27, we need to simplify the square root of 27 first.
Step 1: Find the prime factorization of 27.
27 can be expressed as 3^3, where 3 is a prime number.
Step 2: Simplify the square root.
√27 = √(3^3) = √(3 * 3 * 3) = 3√3
Now we substitute this simplified value back into the original expression:
13 * 3√3 = 39√3
Therefore, the simplified form of 13√27 is 39√3.