Ising a calculator, determine between which two integers the following numbers lie. Then verify your answers by using a calculator 50 \( \begin{array}{llll}30 & \text { (2) } \sqrt{29} & \text { (3) } \sqrt[3]{45} & \text { (4) }-\sqrt{54} \\ \text { (6) } \pi^{4} & \end{array} \)

To find the integers between which each number lies, let's look at them individually: 1. **30**: This is already an integer! It is exactly between 29 and 31 if you want two whole numbers. 2. **\(\sqrt{29}\)**: Since \(5^2 = 25\) and \(6^2 = 36\), we know \(\sqrt{29}\) lies between 5 and 6. Checking with a calculator, \(\sqrt{29} \approx 5.385\), confirming that it indeed lies between 5 and 6. 3. **\(\sqrt[3]{45}\)**: \(3^3 = 27\) and \(4^3 = 64\), so \(\sqrt[3]{45}\) lies between 3 and 4. A calculator gives \(\sqrt[3]{45} \approx 3.556\), which confirms it is between 3 and 4. 4. **\(-\sqrt{54}\)**: Calculating gives us \(-\sqrt{54} \approx -7.348\). Hence, it lies between -8 and -7. 5. **\(\pi^4\)**: Since \(\pi \approx 3.14\), calculating \(\pi^4 \approx 97.67\), so it lies between 97 and 98. Now let's summarize the results: - \(30\): Between 29 and 31 - \(\sqrt{29}\): Between 5 and 6 - \(\sqrt[3]{45}\): Between 3 and 4 - \(-\sqrt{54}\): Between -8 and -7 - \(\pi^4\): Between 97 and 98 With a calculator at hand, you can easily verify these values for the ultimate peace of mind!