1. Problem: Determine if $\sqrt{196}$ is rational or irrational. Step 1: Calculate $\sqrt{196}$. Since $196 = 14^2$, $\sqrt{196} = 14$. Step 2: $14$ is an integer, so it is a rational number. 2. Problem: Determine if $\sqrt{80}$ is rational or irrational. Step 1: Simplify $\sqrt{80}$. $80 = 16 \times 5$, so $\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$. Step 2: Since $\sqrt{5}$ is irrational, $4\sqrt{5}$ is irrational. 3. Problem: Determine if $\sqrt{64}$ is rational or irrational. Step 1: Calculate $\sqrt{64}$. Since $64 = 8^2$, $\sqrt{64} = 8$. Step 2: $8$ is an integer, so it is rational. 4. Problem: Determine if $\sqrt{500}$ is rational or irrational. Step 1: Simplify $\sqrt{500}$. $500 = 100 \times 5$, so $\sqrt{500} = \sqrt{100 \times 5} = \sqrt{100} \times \sqrt{5} = 10\sqrt{5}$. Step 2: Since $\sqrt{5}$ is irrational, $10\sqrt{5}$ is irrational. 5. Problem: Determine if $\sqrt{42}$ is rational or irrational. Step 1: $42$ is not a perfect square, so $\sqrt{42}$ is irrational. 6. Problem: Determine if $\sqrt{81}$ is rational or irrational. Step 1: Calculate $\sqrt{81}$. Since $81 = 9^2$, $\sqrt{81} = 9$. Step 2: $9$ is an integer, so it is rational. 7. Problem: Determine if $\sqrt{18}$ is rational or irrational. Step 1: Simplify $\sqrt{18}$. $18 = 9 \times 2$, so $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$. Step 2: Since $\sqrt{2}$ is irrational, $3\sqrt{2}$ is irrational. 8. Problem: Determine if $2\sqrt{10}$ is rational or irrational. Step 1: $\sqrt{10}$ is irrational because 10 is not a perfect square. Step 2: Multiplying by 2 (a rational number) does not change irrationality, so $2\sqrt{10}$ is irrational. 9. Problem: Determine if $\sqrt{169}$ is rational or irrational. Step 1: Calculate $\sqrt{169}$. Since $169 = 13^2$, $\sqrt{169} = 13$. Step 2: $13$ is an integer, so it is rational. 10. Problem: Determine if $\sqrt{121}$ is rational or irrational. Step 1: Calculate $\sqrt{121}$. Since $121 = 11^2$, $\sqrt{121} = 11$. Step 2: $11$ is an integer, so it is rational. Final answers: 1. Rational 2. Irrational 3. Rational 4. Irrational 5. Irrational 6. Rational 7. Irrational 8. Irrational 9. Rational 10. Rational