To evaluate the equation \((8 - \sqrt{4}) - 24 \cdot (8 - \sqrt{16}) = 8 - 48\), we will calculate each part step by step.
First, we calculate the square roots:
- \(\sqrt{4} = 2\)
- \(\sqrt{16} = 4\)
Now we can substitute these values into the equation:
The left side becomes: \[ (8 - \sqrt{4}) - 24 \cdot (8 - \sqrt{16}) = (8 - 2) - 24 \cdot (8 - 4) \] This simplifies to: \[ 6 - 24 \cdot 4 \] Calculating \(24 \cdot 4\): \[ 24 \cdot 4 = 96 \] So, we have: \[ 6 - 96 = -90 \]
Now, let's evaluate the right side of the equation: \[ 8 - 48 = -40 \]
Now we can compare the two sides:
Left side: \(-90\)
Right side: \(-40\)
Since \(-90 \neq -40\), the equation is false.
Final Answer: False. The left side does not equal the right side.