To determine the correct relationship between \(-3 \sqrt{70}\) and \(-\pi\), we can first calculate the approximate values of both expressions.
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Calculating \(-3 \sqrt{70}\):
- First, we find \(\sqrt{70}\). The square root of 70 is approximately 8.37.
- Then, we calculate \(-3 \sqrt{70}\): \[ -3 \times 8.37 \approx -25.11 \]
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Calculating \(-\pi\):
- The value of \(\pi\) is approximately 3.14.
- Therefore, \(-\pi\) is approximately \(-3.14\).
Now we can compare the values we calculated:
- \(-3 \sqrt{70} \approx -25.11\)
- \(-\pi \approx -3.14\)
Now we can conclude the relationship: \[ -25.11 < -3.14, \] which means: \[ -3 \sqrt{70} < -\pi. \]
Thus, the answer is: \(-3 \sqrt{70} < -\pi\).