Directions: Evaluate the following decimal expression.

$\sqrt{17.64}+0.0729+0.0009+\sqrt{0.000000962361}=?$

The correct answer is 4.273881.

To evaluate the given decimal expression, we calculate each component step-by-step and then add them together:

$\sqrt{17.64}+0.0729+0.0009+\sqrt{0.000000962361}$

Step 1: Evaluate the first term
Convert the decimal 17.64 to a fraction to find its square root easily:

$\sqrt{17.64}=\sqrt{\frac{1764}{100}}=\frac{42}{10}=4.2$

Step 2: Add the intermediate decimal numbers
Combine the second and third decimal terms:

$0.0729+0.0009=0.0738$

Now, add this result to the value obtained from the first term in Step 1:

$4.2+0.0738=4.2738$

Step 3: Evaluate the final square root term
Calculate the value of the last decimal square root term:

$\sqrt{0.000000962361}=0.000081$

Step 4: Perform the final addition
Add the value from Step 3 to the running sum:

$4.2738+0.000081=4.273881$

Thus, the final value of the given expression is 4.273881.