Let's evaluate the expression step by step:
The expression is:
\[
110 - 137 \div \sqrt{3 + 4(-5)^2}
\]
-
Calculate \((-5)^2\):
\[
(-5)^2 = 25
\]
-
Calculate \(4(-5)^2\):
\[
4 \cdot 25 = 100
\]
-
Now calculate \(3 + 100\):
\[
3 + 100 = 103
\]
-
Now take the square root of 103:
\[
\sqrt{103}
\]
-
Next, calculate \(137 \div \sqrt{103}\).
We will keep it as \(\frac{137}{\sqrt{103}}\) for now since the exact decimal would complicate further calculations.
-
Subtract from 110:
\[
110 - \frac{137}{\sqrt{103}}
\]
Now, let's approximate \(\sqrt{103}\):
- The square root of 103 is approximately \(10.148\).
Calculating \(137 \div \sqrt{103}\):
\[
137 \div 10.148 \approx 13.5
\]
Finally, we perform the subtraction:
\[
110 - 13.5 \approx 96.5
\]
None of the options directly match this rounded calculation; thus, it's best to confirm if there's a miscalculation or misinterpretation in the options or expression.
To recap, the overall evaluated value comes to approximately \(97\), rounding from \(96.5\). Based on the given choices, the closest match is:
\[
\boxed{97}
\]