To find two consecutive integers that \(-\sqrt{75}\) lies between, we first calculate \(\sqrt{75}\).
We can simplify \(\sqrt{75}\):
\[ \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \cdot \sqrt{3} = 5\sqrt{3} \]
Next, we need to estimate \(\sqrt{3}\). We know that:
\[ 1.7^2 = 2.89 \quad \text{and} \quad 1.8^2 = 3.24 \]
Thus, we can determine that \(1.7 < \sqrt{3} < 1.8\). To get a more precise value, we can estimate \(\sqrt{3}\) as approximately \(1.732\).
Now, substituting that value back:
\[ \sqrt{75} \approx 5 \times 1.732 = 8.66 \]
Therefore:
\[ -\sqrt{75} \approx -8.66 \]
Now, we need to find the two consecutive integers that \(-8.66\) lies between. The integers that surround \(-8.66\) are \(-9\) and \(-8\).
Thus, \(-\sqrt{75}\) lies between the integers \(-9\) and \(-8\).
In conclusion, \(-\sqrt{75}\) lies between the consecutive integers \(-9\) and \(-8\).