Question 178048
{{{sqrt(6*s*t^2)/sqrt(7*s^3*t)}}} Start with the given expression



{{{(sqrt(6*s*t^2)*sqrt(7*s^3*t))/(sqrt(7*s^3*t)*sqrt(7*s^3*t))}}} Multiply the fraction by {{{sqrt(7*s^3*t)/sqrt(7*s^3*t)}}}



{{{(sqrt(6*s*t^2)*sqrt(7*s^3*t))/(7*s^3*t)}}} Multiply the terms in the denominator.



{{{(sqrt(6*s*t^2*7*s^3*t))/(7*s^3*t)}}} Combine the radicals



{{{(sqrt(42*s^4*t^3))/(7*s^3*t)}}} Multiply



{{{(s^2t*sqrt(42t))/(7*s^3*t)}}} Simplify the square root.



{{{(sqrt(42t))/(7s)}}} Reduce



So {{{sqrt(6*s*t^2)/sqrt(7*s^3*t)=(sqrt(42t))/(7s)}}} where every variable is positive.