Question
If $$\sqrt {{3^n}} = 729$$ , then the value of n is ?
Answer: Option D
$$\eqalign{
& \Leftrightarrow \sqrt {{3^n}} = 729 \cr
& \Leftrightarrow \sqrt {{3^n}} = {3^6} \cr
& \Leftrightarrow {\left( {\sqrt {{3^n}} } \right)^2} = {\left( {{3^6}} \right)^2} \cr
& \Leftrightarrow {3^n} = {3^{12}} \cr
& \Leftrightarrow n = 12 \cr} $$
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$$\eqalign{
& \Leftrightarrow \sqrt {{3^n}} = 729 \cr
& \Leftrightarrow \sqrt {{3^n}} = {3^6} \cr
& \Leftrightarrow {\left( {\sqrt {{3^n}} } \right)^2} = {\left( {{3^6}} \right)^2} \cr
& \Leftrightarrow {3^n} = {3^{12}} \cr
& \Leftrightarrow n = 12 \cr} $$
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