Write the two whole numbers that each square root falls between. Then circle the whole number that the square root is closer to. L32 \( \begin{array}{lll}\text { a. } \sqrt{146} & \text { b. } \sqrt{35} & \text { c. } \sqrt{90}\end{array} \)

**a. Evaluating \( \sqrt{146} \):** 1. Identify two consecutive whole numbers whose squares bound 146: - \(12^2 = 144\) - \(13^2 = 169\) Thus, \( \sqrt{146} \) is between \(12\) and \(13\). 2. Determine which whole number is closer: - Difference from \(12^2\): \(146 - 144 = 2\) - Difference from \(13^2\): \(169 - 146 = 23\) Since \(2 < 23\), \( \sqrt{146} \) is closer to \(12\). **Answer:** \( \textcircled{12} \) and \(13\) --- **b. Evaluating \( \sqrt{35} \):** 1. Identify two consecutive whole numbers whose squares bound 35: - \(5^2 = 25\) - \(6^2 = 36\) Thus, \( \sqrt{35} \) is between \(5\) and \(6\). 2. Determine which whole number is closer: - Difference from \(5^2\): \(35 - 25 = 10\) - Difference from \(6^2\): \(36 - 35 = 1\) Since \(1 < 10\), \( \sqrt{35} \) is closer to \(6\). **Answer:** \(5\) and \( \textcircled{6} \) --- **c. Evaluating \( \sqrt{90} \):** 1. Identify two consecutive whole numbers whose squares bound 90: - \(9^2 = 81\) - \(10^2 = 100\) Thus, \( \sqrt{90} \) is between \(9\) and \(10\). 2. Determine which whole number is closer: - Difference from \(9^2\): \(90 - 81 = 9\) - Difference from \(10^2\): \(100 - 90 = 10\) Since \(9 < 10\), \( \sqrt{90} \) is closer to \(9\). **Answer:** \( \textcircled{9} \) and \(10\)