Question 1
1. option (A) is correct
[tex] \sqrt[3]{32} [/tex]
it equivalent value is
[tex] = \: \sqrt[3]{2×2×2×2×2} [/tex]
[tex] = \: 2\sqrt[3]{4} [/tex]
[tex] \red{ = = = = = = = = = = = = = = = = = = = = = = = }[/tex]
Question 2
2. option (A) is correct
[tex] \sqrt[3]{24 {a}^{6} } [/tex]
[tex]We \: know, \sqrt[n]{ab} = \sqrt[n]{a} \: \sqrt[n]{b} [/tex]
[tex] \sqrt[3]{27a^{6} } = \sqrt[3]{27} . \sqrt[3]{ {a}^{6} } [/tex]
[tex] = \: 3. \sqrt[3]{ {a}^{6} } [/tex]
[tex] = \: 3. {a}^{2} [/tex]
[tex] = \: 3 {a}^{2} [/tex]
[tex] \red{ = = = = = = = = = = = = = = = = = = = = = = = }[/tex]
Question 3
3. option (D) is correct
[tex] \sqrt{ \frac{5}{3} } [/tex]
[tex] = \frac{\sqrt{5}}{ \sqrt{3} } [/tex]
[tex] = \frac{ \sqrt{5}. \sqrt{3} }{ \sqrt{3}. \sqrt{3} } [/tex]
[tex] = \frac{ \sqrt{15} }{ {3} } [/tex]
[tex] \red{ = = = = = = = = = = = = = = = = = = = = = = = }[/tex]
Question 4
4. option (C) is correct
[tex] \sqrt{50} + \sqrt{8} [/tex]
[tex] = \sqrt{ {5}^{2} \times 2} + \sqrt{ {2}^{2} \times 2 } [/tex]
[tex] = \sqrt{ {5}^{2} } \times \sqrt{2} \: + \sqrt{ {2}^{2} } \times \sqrt{2} [/tex]
[tex]5 \sqrt{2} + 2\sqrt{2} [/tex]
[tex] = 7 \sqrt{2} [/tex]
[tex] \red{ = = = = = = = = = = = = = = = = = = = = = = = }[/tex]
Question 5
5. option (B) is correct
[tex] \sqrt{ \frac{8}{15} } = \frac{ \sqrt{8} }{ \sqrt{25} } = \frac{ \sqrt{4 \times 2} }{5} = \frac{ 2\sqrt{2} }{5}[/tex]
[tex] \red{ = = = = = = = = = = = = = = = = = = = = = = }[/tex]
Question 6
6. option (B) is correct
[tex] 9\sqrt{2} - 5 \sqrt{2} = (9 - 5) \sqrt{2} = 4 \sqrt{2} [/tex]
[tex] \red{ = = = = = = = = = = = = = = = = = = = = = = }[/tex]
Question 7
7. option (C) is correct
[tex] \sqrt{36} - 7 \sqrt{ 16} + 4 \sqrt{25} [/tex]
[tex] \sqrt{ {6}^{2} } - 7 \sqrt{ {4}^{2} } + 4 \sqrt{ {5}^{2} } [/tex]
[tex]6 - 7 \times 4 + 4 \times 5[/tex]
[tex]6 - 28 + 20[/tex]
[tex] = - 2[/tex]
[tex] \red{ = = = = = = = = = = = = = = = = = = = = = = }[/tex]
Question 8
8. option (D) is correct
[tex] s = \frac{1}{2}.ah[/tex]
[tex] = \frac{1}{2} \times \sqrt{2x } \sqrt{8} [/tex]
[tex] = \frac{1}{2} \times 4[/tex]
[tex] = 2 \: sq. \: units[/tex]
[tex] \red{ = = = = = = = = = = = = = = = = = = = = = = }[/tex]
Question 9
9. option (C) is correct
Perimeter of rectangle having length l and width b is given by 2L + 2b = 2 (l + b)
[tex]here \: l = \sqrt{75} . \: b = \sqrt{12} [/tex]
[tex]perimeter = 2( \sqrt{75} + \sqrt{12} )[/tex]
[tex] = 2( \sqrt{25 \times 3} + \sqrt{4 \times 3} ) = 2(5 \sqrt{3} + 2 \sqrt{2)} [/tex]
[tex] = 2(7 \sqrt{3} ) = 14 \sqrt{3} [/tex]
[tex] \red{ = = = = = = = = = = = = = = = = = = = = = = = }[/tex]
Question 10
10. option (D) is correct
[tex] \red{ = = = = = = = = = = = = = = = = = = = = = = = }[/tex]
Step-by-step explanation:
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