9) When a positive number is cubed the answer is Before you can root something, you first need to make sure that there is under the root sign. Find the answers to these questions without using your calculator: \( \begin{array}{lll}\text { a) } \sqrt[3]{100+25} & \text { b) } \sqrt{9}+\sqrt{64} & \text { c) } \\ \begin{array}{lll}\text { d) } \sqrt[3]{-216} \\ \text { a) } 20^{2}+(-6)^{3} & \text { e) } \sqrt[3]{9+16} & \text { f) } \sqrt{36}-2^{3}\end{array} \\ \text { (1) })^{3}+\sqrt{81} & \text { h) }(-5)^{2}+(4)^{3} & \text { i) } \sqrt[3]{216}-(-5)^{3}\end{array} \)

Let's solve each part step by step. ### a) \( \sqrt[3]{100 + 25} \) First, we calculate the expression inside the cube root: \[ 100 + 25 = 125 \] Now, we find the cube root: \[ \sqrt[3]{125} = 5 \] ### b) \( \sqrt{9} + \sqrt{64} \) We calculate each square root: \[ \sqrt{9} = 3 \] \[ \sqrt{64} = 8 \] Now, we add the results: \[ 3 + 8 = 11 \] ### c) \( (1)^{3} + \sqrt{81} \) First, we calculate \( (1)^{3} \): \[ (1)^{3} = 1 \] Next, we find the square root: \[ \sqrt{81} = 9 \] Now, we add the results: \[ 1 + 9 = 10 \] ### d) \( \sqrt[3]{-216} \) We find the cube root of \(-216\): \[ \sqrt[3]{-216} = -6 \] ### e) \( \sqrt[3]{9 + 16} \) First, we calculate the expression inside the cube root: \[ 9 + 16 = 25 \] Now, we find the cube root: \[ \sqrt[3]{25} \text{ (This is not a perfect cube, so we leave it as is.)} \] ### f) \( \sqrt{36} - 2^{3} \) First, we calculate the square root: \[ \sqrt{36} = 6 \] Next, we calculate \( 2^{3} \): \[ 2^{3} = 8 \] Now, we subtract: \[ 6 - 8 = -2 \] ### g) \( 20^{2} + (-6)^{3} \) First, we calculate \( 20^{2} \): \[ 20^{2} = 400 \] Next, we calculate \( (-6)^{3} \): \[ (-6)^{3} = -216 \] Now, we add the results: \[ 400 + (-216) = 184 \] ### h) \( (-5)^{2} + (4)^{3} \) First, we calculate \( (-5)^{2} \): \[ (-5)^{2} = 25 \] Next, we calculate \( (4)^{3} \): \[ (4)^{3} = 64 \] Now, we add the results: \[ 25 + 64 = 89 \] ### i) \( \sqrt[3]{216} - (-5)^{3} \) First, we find the cube root: \[ \sqrt[3]{216} = 6 \] Next, we calculate \( (-5)^{3} \): \[ (-5)^{3} = -125 \] Now, we subtract: \[ 6 - (-125) = 6 + 125 = 131 \] ### Summary of Results: - a) \( 5 \) - b) \( 11 \) - c) \( 10 \) - d) \( -6 \) - e) \( \sqrt[3]{25} \) - f) \( -2 \) - g) \( 184 \) - h) \( 89 \) - i) \( 131 \)