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 #2
avatar+1008 
+1
Jul 24, 2019
 #1
avatar+9491 
+5

\((4-a)^3\ =\ 32\)

                                         Take the cube root of both sides of the equation.

\(\sqrt[3]{(4-a)^3}\ =\ \sqrt[3]{32}\)

                                         Simplify the left side with the rule  \(\sqrt[3]{n^3}\ =\ n\)

\(4-a\ =\ \sqrt[3]{32}\)

                                                    We can rewrite  32  like this because  32 = 2 * 2 * 2 * 2 * 2

\(4-a\ =\ \sqrt[3]{2\cdot2\cdot2\cdot2\cdot2}\)

                                                    We can rewrite the right side again like this...

\(4-a\ =\ \sqrt[3]{2\cdot2\cdot2}\cdot\sqrt[3]{2\cdot2}\)

                                                    And   2 * 2 * 2  =  23   and   2 * 2  =  4

\(4-a\ =\ \sqrt[3]{2^3}\,\cdot\,\sqrt[3]{4}\)

                                                    Simplify  \(\sqrt[3]{2^3}\)  again with the rule  \(\sqrt[3]{n^3}\ =\ n\)

\(4-a\ =\ 2\,\cdot\,\sqrt[3]{4}\)

 

\(4-a\ =\ 2\sqrt[3]{4}\)

                               Add  a  to both sides of the equation.

\(4\ =\ 2\sqrt[3]{4}+a\)

                               Subtract  \(2\sqrt[3]{4}\)  from both sides of the equation.

\(4-2\sqrt[3]{4}\ =\ a\)

 

\(a\ =\ 4-2\sqrt[3]{4}\)-

Jul 24, 2019
 #6
avatar+37171 
0
Jul 24, 2019

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