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