[tex]if \: \sqrt[3]{32768} = 32 \: then \: [/tex]
[tex]i) \: \sqrt[3]{0.032786} = [/tex]
[tex]ii) \: \sqrt[3]{32.768} = [/tex]
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[tex]if \: \sqrt[3]{32768} = 32 \: then \: [/tex]
[tex]i) \: \sqrt[3]{0.032786} = [/tex]
[tex]ii) \: \sqrt[3]{32.768} = [/tex]
give me answer
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Appropriate Question :-
[tex]If \: \sqrt[3]{32768} = 32 \: then \: [/tex]
[tex](i) \: \sqrt[3]{0.032768} = [/tex]
[tex](ii) \: \sqrt[3]{32.768} = [/tex]
Answer:
[tex]\qquad \:\boxed{\begin{aligned}& \qquad \:\sf \: (i) \: \: \sqrt[3]{0.032768} =0.32 \qquad \: \\ \\& \qquad \:\sf \: (ii) \: \: \sqrt[3]{32.768} =3.2\end{aligned}} \qquad \\ \\ [/tex]
Step-by-step explanation:
Given that,
[tex]\sf \: \sqrt[3]{32768} = 32 \\ \\ [/tex]
Now, Consider
[tex]\bf \: \sqrt[3]{0.032768} \\ \\ [/tex]
can be rewritten as
[tex]\sf \: = \: \sqrt[3]{\dfrac{32768}{1000000} } \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{ \sqrt[3]{32768} }{ \sqrt[3]{1000000} } \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{ \sqrt[3]{32768} }{ \sqrt[3]{100 \times 100 \times 100} } \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{32}{100} \\ \\ [/tex]
[tex]\sf \: = \: 0.32 \\ \\ [/tex]
Hence,
[tex]\bf\implies \: \sqrt[3]{0.032768} = \: 0.32 \\ \\ \\ [/tex]
Now, Consider
[tex]\bf \: \sqrt[3]{32.768} \\ \\ [/tex]
can be rewritten as
[tex]\sf \: = \: \sqrt[3]{\dfrac{32768}{1000} } \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{ \sqrt[3]{32768} }{ \sqrt[3]{1000} } \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{ \sqrt[3]{32768} }{ \sqrt[3]{10 \times 10 \times 10} } \\ \\ [/tex]
[tex]\sf \: = \: \dfrac{32}{10} \\ \\ [/tex]
[tex]\sf \: = \: 3.2 \\ \\ [/tex]
Hence,
[tex]\bf\implies \: \sqrt[3]{32.768} = \: 3.2 \\ \\ \\ [/tex]
[tex]\rule{190pt}{2pt}\rule{190pt}{2pt}[/tex]
Additional Information
[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]