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Answer :
Sure! Let's go through each of the questions step-by-step.
### Question 25:
Find the value of [tex]\(\sqrt{a^2+b^2}\)[/tex] where [tex]\(a = 3\)[/tex] and [tex]\(b = 4\)[/tex].
1. Calculate [tex]\(a^2 = 3^2 = 9\)[/tex].
2. Calculate [tex]\(b^2 = 4^2 = 16\)[/tex].
3. Add the squares: [tex]\(a^2 + b^2 = 9 + 16 = 25\)[/tex].
4. Find the square root: [tex]\(\sqrt{25} = 5\)[/tex].
Answer: B. 5
### Question 26:
Simplify [tex]\(\frac{\sqrt{200}}{2}\)[/tex].
1. Calculate the square root: [tex]\(\sqrt{200} = \sqrt{(100 \times 2)} = 10\sqrt{2}\)[/tex].
2. Simplify [tex]\(\frac{10\sqrt{2}}{2} = 5\sqrt{2}\)[/tex].
Answer: B. [tex]\(5\sqrt{2}\)[/tex]
### Question 27:
Identify which statement is not true:
- A. [tex]\(\frac{\sqrt[3]{8}}{27}=\frac{2}{3}\)[/tex]
- B. [tex]\(\frac{\sqrt{45}}{3}=\sqrt{5}\)[/tex]
- C. [tex]\(\sqrt[3]{\frac{-1}{9}}=-\frac{1}{3}\)[/tex]
- D. [tex]\(\sqrt{100}\)[/tex]
To find the incorrect statement:
- Check each calculation:
- (A) is not true: [tex]\(\sqrt[3]{8} = 2\)[/tex] and thus [tex]\(\frac{2}{27}\)[/tex] does not equal [tex]\(\frac{2}{3}\)[/tex].
- Other statements are correct as verified by calculations.
Answer: A
### Question 28:
Which one of the following is a perfect square?
- A. 27
- B. 81
- C. -343
- D. 50
Perfect squares are numbers like [tex]\(1, 4, 9, 16, 25, 36, 49, 64, 81, \ldots\)[/tex].
- 81 is a perfect square because [tex]\(9^2 = 81\)[/tex].
Answer: B. 81
### Question 29:
Calculate [tex]\(x^3\)[/tex] where [tex]\(x=0.9\)[/tex].
1. [tex]\(x^3 = 0.9^3\)[/tex].
2. Calculate the cube: [tex]\(0.9 \times 0.9 \times 0.9 = 0.729\)[/tex].
Answer: B. 0.729
### Question 30:
Which one of the following is a perfect cube?
- A. 0
- B. 28
- C. 16
- D. 81
Perfect cubes are numbers like [tex]\(0, 1, 8, 27, 64,\ldots\)[/tex].
- 0 is a perfect cube because [tex]\(0^3 = 0\)[/tex].
Answer: A. 0
### Question 25:
Find the value of [tex]\(\sqrt{a^2+b^2}\)[/tex] where [tex]\(a = 3\)[/tex] and [tex]\(b = 4\)[/tex].
1. Calculate [tex]\(a^2 = 3^2 = 9\)[/tex].
2. Calculate [tex]\(b^2 = 4^2 = 16\)[/tex].
3. Add the squares: [tex]\(a^2 + b^2 = 9 + 16 = 25\)[/tex].
4. Find the square root: [tex]\(\sqrt{25} = 5\)[/tex].
Answer: B. 5
### Question 26:
Simplify [tex]\(\frac{\sqrt{200}}{2}\)[/tex].
1. Calculate the square root: [tex]\(\sqrt{200} = \sqrt{(100 \times 2)} = 10\sqrt{2}\)[/tex].
2. Simplify [tex]\(\frac{10\sqrt{2}}{2} = 5\sqrt{2}\)[/tex].
Answer: B. [tex]\(5\sqrt{2}\)[/tex]
### Question 27:
Identify which statement is not true:
- A. [tex]\(\frac{\sqrt[3]{8}}{27}=\frac{2}{3}\)[/tex]
- B. [tex]\(\frac{\sqrt{45}}{3}=\sqrt{5}\)[/tex]
- C. [tex]\(\sqrt[3]{\frac{-1}{9}}=-\frac{1}{3}\)[/tex]
- D. [tex]\(\sqrt{100}\)[/tex]
To find the incorrect statement:
- Check each calculation:
- (A) is not true: [tex]\(\sqrt[3]{8} = 2\)[/tex] and thus [tex]\(\frac{2}{27}\)[/tex] does not equal [tex]\(\frac{2}{3}\)[/tex].
- Other statements are correct as verified by calculations.
Answer: A
### Question 28:
Which one of the following is a perfect square?
- A. 27
- B. 81
- C. -343
- D. 50
Perfect squares are numbers like [tex]\(1, 4, 9, 16, 25, 36, 49, 64, 81, \ldots\)[/tex].
- 81 is a perfect square because [tex]\(9^2 = 81\)[/tex].
Answer: B. 81
### Question 29:
Calculate [tex]\(x^3\)[/tex] where [tex]\(x=0.9\)[/tex].
1. [tex]\(x^3 = 0.9^3\)[/tex].
2. Calculate the cube: [tex]\(0.9 \times 0.9 \times 0.9 = 0.729\)[/tex].
Answer: B. 0.729
### Question 30:
Which one of the following is a perfect cube?
- A. 0
- B. 28
- C. 16
- D. 81
Perfect cubes are numbers like [tex]\(0, 1, 8, 27, 64,\ldots\)[/tex].
- 0 is a perfect cube because [tex]\(0^3 = 0\)[/tex].
Answer: A. 0
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