Express in simplest radical form
8x square root 5x^5 + x^3 square root 45x
To express the expression in simplest radical form, we can simplify each radical separately.
First, let's simplify the radical √5x^5.
We can break down x^5 as x^4 * x, and since we're taking the square root, we can break that down further as x^2 * x * x.
Since the square root of x^2 is x, the simplified radical becomes x^2 * √(5x).
Next, we simplify the radical √45x.
To simplify the radical, we need to find the largest perfect square that can be divided into 45.
The largest perfect square that divides 45 is 9, which is 3^2.
So we can write the expression as: x^2 * √(5x) + x^3 * √(9x).
Finally, simplify the expression by simplifying the square root of 9 to 3: x^2 * √(5x) + 3x^3 * √(x).
This is the simplest radical form of the expression.