To evaluate the equation \((8 - \sqrt{4}) - 24 \cdot (8 - \sqrt{16}) = 8 - 48\), let's simplify both sides step by step.
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Calculate \(\sqrt{4}\) and \(\sqrt{16}\):
- \(\sqrt{4} = 2\)
- \(\sqrt{16} = 4\)
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Substitute these values back into the equation: \[(8 - 2) - 24 \cdot (8 - 4) = 8 - 48\]
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Simplify the left side:
- \(8 - 2 = 6\)
- \(8 - 4 = 4\)
- So, \(24 \cdot 4 = 96\)
Now, substitute back in: \[6 - 96\]
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Continue to simplify: \[6 - 96 = -90\]
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Now simplify the right side: \[8 - 48 = -40\]
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Put it all together: We now have: \[-90 \text{ (left side)} \quad \text{and} \quad -40 \text{ (right side)}\]
Since \(-90 \neq -40\), the equation is false.
Final answer: False. The left side equals \(-90\) whereas the right side equals \(-40\).
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