Express in simplest radical form
2x square root 48x^3 + 9 square root 3x^5
To simplify the expression 2x√(48x^3) + 9√(3x^5), we can simplify each radical separately.
First, let's simplify √(48x^3). We can break down 48x^3 as the product of a perfect square and the remaining factors. The largest perfect square factor of 48 is 16, which is the square of 4. Additionally, x^3 can be written as x^2 * x. Therefore, we have:
√(48x^3) = √(16 * 3 * x^2 * x) = 4x√(3x).
Next, let's simplify √(3x^5). We can break down x^5 as the product of a perfect square and the remaining factors. The largest perfect square factor of x^5 is x^4, which is the square of x^2. Therefore, we have:
√(3x^5) = √(3 * x^4 * x) = x^2√(3x).
Now, we can rewrite the expression 2x√(48x^3) + 9√(3x^5) as:
2x(4x√(3x)) + 9(x^2√(3x)) = 8x^2√(3x) + 9x^2√(3x).
Since both terms have a common factor of x^2√(3x), we can factor this term out:
8x^2√(3x) + 9x^2√(3x) = (8x^2 + 9x^2)√(3x) = 17x^2√(3x).
Therefore, the expression 2x√(48x^3) + 9√(3x^5) simplified in simplest radical form is 17x^2√(3x).