Question

If √2ⁿ = 1024, find the value of 3² × n

Answer 1

$\rm{ \sqrt{2^{n}} = 1024}$

$\rm{\sqrt{ {2}^{n} } = {2}^{10} } \\ \texttt{squaring \: both \: sides} \\ \rm{ {2}^{n} = {2}^{20} }$

$\rm{ \cancel{2}^n = \cancel{2}^{20}} \\ \rm{n \: = 20}$

$\rm \pink{ {3}^{2} \times 20 = 9 \times 20 = 180}$

Answer 2

$\rm{ \sqrt{2^{n}} = 1024}$

$\rm{\sqrt{ {2}^{n} } = {2}^{10} } \\ \texttt{squaring \: both \: sides} \\ \rm{ {2}^{n} = {2}^{20} }$

$\rm{ \cancel{2}^n = \cancel{2}^{20}} \\ \rm{n \: = 20}$

$\rm \orange{ {3}^{2} \times 20 = 9 \times 20 = 180}$