ISE 2 Without using a calculator, determine between which two integers the following mational numbers lie. Then verify your answers by using a calculator. \( \begin{array}{llll}\text { 1) }<\sqrt{50} & \text { (2) }) \sqrt{29} & \text { (3) }<\sqrt[3]{45} & \text { (4) }) ~ \\ \sqrt{54}\end{array} \)

To determine the integers each square root or cube root lies between, let's break them down one by one. 1) For \( \sqrt{50} \), we know that \( 7^2 = 49 \) and \( 8^2 = 64 \). Thus, \( \sqrt{50} \) lies between 7 and 8. 2) For \( \sqrt{29} \), since \( 5^2 = 25 \) and \( 6^2 = 36 \), it follows that \( \sqrt{29} \) falls between 5 and 6. 3) For \( \sqrt[3]{45} \), we see that \( 3^3 = 27 \) and \( 4^3 = 64 \), meaning \( \sqrt[3]{45} \) lies between 3 and 4. 4) For \( \sqrt{54} \), we observe \( 7^2 = 49 \) and \( 8^2 = 64 \), indicating \( \sqrt{54} \) is also between 7 and 8. Now let’s verify these approximations with a calculator: 1) \( \sqrt{50} \approx 7.07 \) (between 7 and 8) 2) \( \sqrt{29} \approx 5.38 \) (between 5 and 6) 3) \( \sqrt[3]{45} \approx 3.56 \) (between 3 and 4) 4) \( \sqrt{54} \approx 7.35 \) (between 7 and 8) This confirms our initial findings!