Calculate these roots: a) [3]1000 - [3]125, b) [3]64, c) sqrt(25 - 16), d) sqrt(100 - 64). Compare these calculations. Replace with >, < or =. a) 23 32

Here are the solutions to your math problems: 5. Calculate these roots: (Note: The instruction says "cube roots", but the symbols for c) and d) are square roots. I will solve a) and b) as cube roots and c) and d) as square roots, following the notation shown.) a) [3]1000 - [3]125 Step 1: Calculate the cube roots. [3]1000 = 10 [3]125 = 5 Step 2: Subtract the results. 10 - 5 = 5 The answer is 5. b) [3]64 Step 1: Find the number that, when multiplied by itself three times, equals 64. 4 × 4 × 4 = 64 The answer is 4. c) sqrt(25 - 16) Step 1: Perform the subtraction inside the square root. 25 - 16 = 9 Step 2: Calculate the square root of the result. sqrt(9) = 3 The answer is 3. d) sqrt(100 - 64) Step 1: Perform the subtraction inside the square root. 100 - 64 = 36 Step 2: Calculate the square root of the result. sqrt(36) = 6 The answer is 6. 6. Compare these calculations. Replace with >, < or =. a) 2^3 3^2 Step 1: Calculate 2^3. 2^3 = 2 × 2 × 2 = 8 Step 2: Calculate 3^2. 3^2 = 3 × 3 = 9 Step 3: Compare the values. 8 < 9 The comparison is 2^3 < 3^2. b) 2 × 4 2^4 Step 1: Calculate 2 × 4. 2 × 4 = 8 Step 2: Calculate 2^4. 2^4 = 2 × 2 × 2 × 2 = 16 Step 3: Compare the values. 8 < 16 The comparison is 2 × 4 < 2^4. c) 8 × 8 8^2 Step 1: Calculate 8 × 8. 8 × 8 = 64 Step 2: Calculate 8^2. 8^2 = 8 × 8 = 64 Step 3: Compare the values. 64 = 64 The comparison is 8 × 8 = 8^2. d) 9^2 9 × 2 Step 1: Calculate 9^2. 9^2 = 9 × 9 = 81 Step 2: Calculate 9 × 2. 9 × 2 = 18 Step 3: Compare the values. 81 > 18 The comparison is 9^2 > 9 × 2. e) 7^2 7^3 Step 1: Calculate 7^2. 7^2 = 7 × 7 = 49 Step 2: Calculate 7^3. 7^3 = 7 × 7 × 7 = 343 Step 3: Compare the values. 49 < 343 The comparison is 7^2 < 7^3. f) [3]8 [3]27 Step 1: Calculate [3]8. [3]8 = 2 Step 2: Calculate [3]27. [3]27 = 3 Step 3: Compare the values. 2 < 3 The comparison is [3]8 < [3]27. g) 6^3 5^4 Step 1: Calculate 6^3. 6^3 = 6 × 6 × 6 = 216 Step 2: Calculate 5^4. 5^4 = 5 × 5 × 5 × 5 = 625 Step 3: Compare the values. 216 < 625 The comparison is 6^3 < 5^4. 7. Mr Tladi wants to pave his verandah. a) If the length of his verandah is 4 m and the breadth is 3 m, how many m^2 of bricks does he need? Step 1: Identify the formula for the area of a rectangle. Area = length × breadth Step 2: Substitute the given values. Area = 4 m × 3 m Step 3: Calculate the area. Area = 12 m^2 Mr Tladi needs 12 m^2 of bricks. b) Mr Tladi needs sand to do his paving. If the truck measures 3 m by 2 m by 1 m, how many m^3 of sand can it hold? Step 1: Identify the formula for the volume of a rectangular prism. Volume = length × breadth × height Step 2: Substitute the given dimensions of the truck. $Volume = 3 m × 2