Between which two consecutive integers do the following irrational numbers lie? \( \begin{array}{lll}\text { (1) } \sqrt{7} & \text { (2) }-\sqrt{3} & \text { (3) } \sqrt{97}\end{array} \)

To find the consecutive integers for each of the irrational numbers: 1. For \( \sqrt{7} \), we know that \( 2^2 = 4 \) and \( 3^2 = 9 \). Thus, \( 2 < \sqrt{7} < 3 \). Therefore, \( \sqrt{7} \) lies between the integers 2 and 3. 2. For \( -\sqrt{3} \), note that \( \sqrt{3} \) is approximately 1.732. Thus, \( -\sqrt{3} \) is approximately -1.732, positioning it between -2 and -1. Therefore, \( -\sqrt{3} \) lies between the integers -2 and -1. 3. For \( \sqrt{97} \), we know \( 9^2 = 81 \) and \( 10^2 = 100 \). Thus, \( 9 < \sqrt{97} < 10 \). Therefore, \( \sqrt{97} \) lies between the integers 9 and 10. In summary, the irrational numbers lie between: - \( \sqrt{7} \) is between 2 and 3. - \( -\sqrt{3} \) is between -2 and -1. - \( \sqrt{97} \) is between 9 and 10.