We need to evaluate the expression $\frac{3}{8} \sqrt{6^2 + 8^2} + (1.5)^2$.

1. Problem Description

We need to evaluate the expression $\frac{3}{8} \sqrt{6^2 + 8^2} + (1.5)^2$.

2. Solution Steps

First, we calculate $6^2$ and $8^2$.

$6^2 = 6 \times 6 = 36$

$8^2 = 8 \times 8 = 64$

Next, we calculate the sum of $6^2$ and $8^2$.

$6^2 + 8^2 = 36 + 64 = 100$

Now, we take the square root of the sum.

$\sqrt{6^2 + 8^2} = \sqrt{100} = 10$

Then, we multiply the result by $\frac{3}{8}$.

$\frac{3}{8} \sqrt{6^2 + 8^2} = \frac{3}{8} \times 10 = \frac{30}{8} = \frac{15}{4}$

Now we need to calculate $(1.5)^2$.

$(1.5)^2 = 1.5 \times 1.5 = 2.25$

Finally, we add the two terms together.

$\frac{3}{8} \sqrt{6^2 + 8^2} + (1.5)^2 = \frac{15}{4} + 2.25 = \frac{15}{4} + \frac{9}{4} = \frac{24}{4} = 6$

3. Final Answer

6