Find radius of the circle `(x−2)^2+(y−3)^2=(5sqrt5)^2`

Answer

To find the radius of the circle given by the equation \((x−2)^2+(y−3)^2=(5\sqrt{5})^2\), we can follow these steps:

### Step 1: Identify the standard form of the circle's equation
The standard form of the equation of a circle is given by:
\[ (x - x_1)^2 + (y - y_1)^2 = r^2 \]
where \((x_1, y_1)\) is the center of the circle and \(r\) is the radius.

### Step 2: Compare the given equation with the standard form
The given equation is:
\[ (x - 2)^2 + (y - 3)^2 = (5\sqrt{5})^2 \]
Here, we can see that:
- \(x_1 = 2\)
- \(y_1 = 3\)
- \(r^2 = (5\sqrt{5})^2\)

### Step 3: Calculate \(r^2\)
To find the radius, we need to calculate \(r\):
\[ r^2 = (5\sqrt{5})^2 \]
Calculating this gives:
\[ r^2 = 5^2 \cdot (\sqrt{5})^2 = 25 \cdot 5 = 125 \]

### Step 4: Find the radius \(r\)
Now, we take the square root of \(r^2\) to find \(r\):
\[ r = \sqrt{125} \]
We can simplify \(\sqrt{125}\):
\[ r = \sqrt{25 \cdot 5} = \sqrt{25} \cdot \sqrt{5} = 5\sqrt{5} \]

### Final Answer
Thus, the radius of the circle is:
\[ \boxed{5\sqrt{5}} \]