Which sign makes the statement true?

Question

–3 (the square root of sign)70 ? –𝜋
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Answer 1

To determine the correct relationship between \(-3 \sqrt{70}\) and \(-\pi\), we can first calculate the approximate values of both expressions.

1. Calculating \(-3 \sqrt{70}\):

   • First, we find \(\sqrt{70}\). The square root of 70 is approximately 8.37.
   • Then, we calculate \(-3 \sqrt{70}\): \[ -3 \times 8.37 \approx -25.11 \]

2. 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: \(-3 \sqrt{70} < -\pi\).