To determine the relation between \(-\sqrt{40}\) and \(-4\pi\), we first need to calculate the numerical values of both expressions.
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Calculate \(-\sqrt{40}\): \[ \sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10} \] To approximate \(\sqrt{10}\): \(\sqrt{10} \approx 3.16\), so: \[ \sqrt{40} \approx 2 \times 3.16 \approx 6.32 \] Therefore: \[ -\sqrt{40} \approx -6.32 \]
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Calculate \(-4\pi\): Using \(\pi \approx 3.14\): \[ -4\pi \approx -4 \times 3.14 \approx -12.56 \]
Now, we compare the two values: \[ -6.32 \text{ (which is } -\sqrt{40}) \text{ and } -12.56 \text{ (which is } -4\pi). \]
Since \(-6.32\) is greater than \(-12.56\), we have: \[ -\sqrt{40} > -4\pi \]
Thus, the correct sign that makes the statement true is >.
So the final answer is: \[ -\sqrt{40} > -4\pi \]