Calculate the sum in the numerator.

$$\frac{14.8}{0.144}$$

To simplify the division, multiply both the numerator and the denominator by 1000 to remove the decimals:

$$\frac{14.8 \times 1000}{0.144 \times 1000} = \frac{14800}{144}$$

$$\frac{14800}{144} = 102.777...$$

Rounding to four decimal places:

$$102.777... \approx 102.7778$$

The value is $\boxed{\text{102.7778}}$.

11. Use a table to look for a square root of 0.8236

To find the square root of 0.8236 using a table, you would locate 0.8236 in the table's appropriate column (e.g., for square roots of numbers between 0 and 1).
Calculating the square root directly:

$$\sqrt{0.8236} \approx 0.9075241$$

Rounding to four decimal places, as is common for table values:

$$\sqrt{0.8236} \approx 0.9075$$

The square root of 0.8236 is approximately $\boxed{\text{0.9075}}$.

12. Evaluate: $\frac{3}{8}$ of $\left[7\frac{3}{5} - \frac{1}{3}\left(1\frac{1}{4} + 3\frac{1}{3} \times 2\frac{2}{5}\right)\right]$

$$7\frac{3}{5} = \frac{7 \times 5 + 3}{5} = \frac{38}{5}$$ $$1\frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4}$$ $$3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3}$$ $$2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5}$$

Substitute these into the expression:

$$\frac{3}{8} \times \left[\frac{38}{5} - \frac{1}{3}\left(\frac{5}{4} + \frac{10}{3} \times \frac{12}{5}\right)\right]$$

$$\frac{5}{4} + 8 = \frac{5}{4} + \frac{32}{4} = \frac{37}{4}$$

The expression now becomes:

$$\frac{3}{8} \times \left[\frac{38}{5} - \frac{1}{3}\left(\frac{37}{4}\right)\right]$$

$$\frac{1}{3} \times \frac{37}{4} = \frac{37}{12}$$

The expression now becomes:

$$\frac{3}{8} \times \left[\frac{38}{5} - \frac{37}{12}\right]$$

Find a common denominator for 5 and 12, which is 60.

$$\frac{38}{5} - \frac{37}{12} = \frac{38 \times 12}{5 \times 12} - \frac{37 \times 5}{12 \times 5} = \frac{456}{60} - \frac{185}{60} = \frac{456 - 185}{60} = \frac{271}{60}$$

The expression now becomes:

$$\frac{3}{8} \times \frac{271}{60}$$

$$\frac{3}{8} \times \frac{271}{60} = \frac{3 \times 271}{8 \times 60}$$

We can simplify by dividing 3 and 60 by their common factor, 3:

$$\frac{1 \times 271}{8 \times 20} = \frac{271}{160}$$

As a mixed number:

$$1\frac{111}{160}$$

The evaluated expression is $\boxed{\frac{271}{160}}$ or $\boxed{1\frac{111}{160}}$.