Let's break down the expression step by step:
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Identifying the components of the expression: The expression is given as \( 110 - 137 - \sqrt{3 + 4(-5)^2} \).
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Calculating \( (-5)^2 \): \[ (-5)^2 = 25 \]
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Calculating \( 4(-5)^2 \): \[ 4 \times 25 = 100 \]
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Calculating \( 3 + 4(-5)^2 \): \[ 3 + 100 = 103 \]
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Calculating \( \sqrt{103} \): The square root of 103 is an irrational number. Let's simplify the expression up to this point instead of calculating the exact value.
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Substituting back into the expression: \[ 110 - 137 - \sqrt{103} \]
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Calculating \( 110 - 137 \): \[ 110 - 137 = -27 \]
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Final expression: \[ -27 - \sqrt{103} \]
At this point, we can evaluate the approximate value of \( \sqrt{103} \). The square root of 103 is approximately \( 10.14 \).
- Final calculation: \[ -27 - 10.14 \approx -37.14 \]
Given the choices (97, 103, 37), it seems none of the exact values match our calculated result. If there was an oversight in interpretation or further simplification was required, please provide clarification. If only approximations are considered, the closest correct option based on calculations can be about -37, but not directly given in the options.
Given the options presented, I would summarize it as none of the above responses are correct. Could you clarify any part of the question or provide more context?