Find the average rate of change of the function $f(x)=\sqrt{x}$ from $x_{1}=36$ to $x_{2}=49$. The average rate of change is (Simplify your answer.)

Step 1 ：Given the function \(f(x) = \sqrt{x}\) and two points \(x_1 = 36\) and \(x_2 = 49\).

Step 2 ：The average rate of change of a function between two points is given by the formula: \[\frac{f(x_2) - f(x_1)}{x_2 - x_1}\]

Step 3 ：Substitute the given values into the formula: \[\frac{f(49) - f(36)}{49 - 36}\]

Step 4 ：Calculate the values of \(f(x_1)\) and \(f(x_2)\): \[f(36) = \sqrt{36} = 6.0\] and \[f(49) = \sqrt{49} = 7.0\]

Step 5 ：Substitute these values into the formula: \[\frac{7.0 - 6.0}{49 - 36}\]

Step 6 ：Simplify the expression to find the average rate of change: \[0.07692307692307693\]

Step 7 ：So, the average rate of change of the function \(f(x) = \sqrt{x}\) from \(x_1 = 36\) to \(x_2 = 49\) is approximately \(0.0769\).

Step 8 ：Final Answer: The average rate of change of the function \(f(x) = \sqrt{x}\) from \(x_1 = 36\) to \(x_2 = 49\) is \(\boxed{0.0769}\)