12 Fill in the blanks with \( < \),\( \rangle , or = \) to correctly compare the expressions. \( \sqrt{7}+9-7+\sqrt{9} \) \( \sqrt{35}-\sqrt[3]{115} \)

To solve the comparison, let's evaluate both expressions. For the first expression, \( \sqrt{7}+9-7+\sqrt{9} \): - \( \sqrt{7} \) is approximately \( 2.645751311 \), and \( \sqrt{9} = 3 \). - So, it becomes: \[ \sqrt{7} + 9 - 7 + 3 \approx 2.645751311 + 9 - 7 + 3 = 2.645751311 + 5 \approx 7.645751311. \] For the second expression, \( \sqrt{35}-\sqrt[3]{115} \): - \( \sqrt{35} \) is approximately \( 5.916079783 \), and \( \sqrt[3]{115} \) is approximately \( 4.820 \). - So, it becomes: \[ \sqrt{35} - \sqrt[3]{115} \approx 5.916079783 - 4.820 \approx 1.096079783. \] Now we can compare: - The value of the first expression is approximately \( 7.645751311 \), and the value of the second expression is approximately \( 1.096079783 \). Thus, we can conclude that: \[ \sqrt{7}+9-7+\sqrt{9} > \sqrt{35}-\sqrt[3]{115} \] So, the correct inequality is: \( \sqrt{7}+9-7+\sqrt{9} > \sqrt{35}-\sqrt[3]{115} \) or \( 7.645751311 > 1.096079783 \). Thus, the fill would be: \( < \)