Question 1086951
<font color="black" face="times" size="3">{{{L=i * sqrt(1-v^2/c^2) }}}


{{{L/i=(i * sqrt(1-v^2/c^2))/i }}} Divide both sides by 'i'


{{{L/i=sqrt(1-v^2/c^2) }}} 


{{{(L/i)^2=(sqrt(1-v^2/c^2))^2 }}} Square both sides


{{{(L/i)^2=1-v^2/c^2 }}}


{{{(L/i)^2-1=1-v^2/c^2-1 }}} Subtract 1 from both sides


{{{(L/i)^2-1=-v^2/c^2 }}}


{{{-c^2((L/i)^2-1)=-c^2(-v^2/c^2) }}} Multiply both sides by -c^2


{{{-c^2((L/i)^2-1)=v^2 }}}


{{{v^2 = -c^2((L/i)^2-1)}}}


{{{v = ""+-sqrt(-c^2((L/i)^2-1))}}} Apply the square root to both sides


{{{v = sqrt(-c^2((L/i)^2-1))}}} You can drop the plus minus sign assuming {{{ v >= 0}}}


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