Question

State which of the following option is true.

$a. \sqrt[3]{ \frac{125 \times 64}{0.001331} } = \frac{2000}{11} \\ \\ b. \sqrt[3]{216} - \sqrt[3]{0.027} + \sqrt[3]{0.125} = 6.8 \\ \\ c. \: \sqrt[3]{ \frac{0.512}{0.064} } \div \sqrt[3]{0.008} = 10$
Options :-
a) only a
b) only c
c) both a and c
d) All a, b and c​

Answer 1

Answer:

the answer is a

Step-by-step explanation:

a.

3

0.001331

125×64

=

11

2000

Answer 2

$\bf \:\large \red{AηsωeR : a} ✍$

$\tt \: Consider \: LHS \: : \sqrt[3]{ \dfrac{125 \times 64}{0.001331} }$

$\tt \: = \sqrt[3]{ \dfrac{125 \times 64 \times 1000000}{1331} }$

$\tt \: = \sqrt[3]{ \dfrac{5 \times 5 \times 5 \times 4 \times \times 4 \times 4 \times 100 \times 100 \times 100}{11 \times 11 \times 11} }$

$\tt \: = \dfrac{5 \times 4 \times 100 }{11} = \dfrac{2000}{11}$

$\bf\implies \:➦ LHS = RHS$

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$\bf \:\large \red{AηsωeR : b} ✍$

$\tt \: \sqrt[3]{216} - \sqrt[3]{0.027} + \sqrt[3]{0.125} = 6.8$

$\tt \: Consider \: LHS \: \sqrt[3]{216} - \sqrt[3]{0.027} + \sqrt[3]{0.125}$

$\tt \: = \sqrt[3]{6 \times 6 \times 6} - \sqrt[3]{\dfrac{27}{1000} } + \sqrt[3]{\dfrac{125}{1000} }$

$\tt \: = 6 - \sqrt[3]{\dfrac{3 \times 3 \times 3}{10 \times 10 \times 10} } + \sqrt[3]{\dfrac{5 \times 5 \times 5}{10 \times 10 \times 10} }$

$\tt \: = 6 - \dfrac{3}{10} + \dfrac{5}{10}$

$\tt \: = \dfrac{60 - 3 + 5}{10} = \dfrac{62}{10} = 6.2$

$\bf \:  ➦ LHS ≠ RHS$

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$\bf \:\large \red{AηsωeR : c} ✍$

$\tt \: \: \sqrt[3]{ \dfrac{0.512}{0.064} } \div \sqrt[3]{0.008} = 10$

$\tt \: Consider \: LHS \: \tt \: \: \sqrt[3]{ \dfrac{0.512}{0.064} } \div \sqrt[3]{0.008}$

$\tt \: \: = \sqrt[3]{ \dfrac{512}{64} } \div \sqrt[3]{ \dfrac{8}{1000} }$

$\tt \: \: = \sqrt[3]{ \dfrac{8 \times 8 \times 8}{4 \times 4 \times 4} } \div \sqrt[3]{ \dfrac{2 \times 2 \times 2}{10 \times 10 \times 10} }$

$\tt \: = 2 \div \dfrac{2}{10}$

$\tt \: = 10$

$\bf \:  ➦ LHS = RHS$

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$\large{\boxed{\boxed{\bf{Option \: (c) \: is \: correct}}}}$