Question 96563
{{{sqrt((1/9+2/3)/(4/25+3/5))}}} Start with the given expression



{{{sqrt((1/9+(2/3)(3/3))/(4/25+3/5))}}} Multiply {{{2/3}}} by {{{3/3}}} 



{{{sqrt((1/9+6/9)/(4/25+3/5))}}} Multiply {{{2/3}}} and {{{3/3}}} to get{{{6/9}}} 



{{{sqrt((1/9+6/9)/(4/25+(3/5)(5/5)))}}} Multiply {{{3/5}}} by {{{5/5}}} 



{{{sqrt((1/9+6/9)/(4/25+15/25))}}} Multiply {{{3/5}}} and {{{5/5}}} to get{{{15/25}}} 




{{{sqrt((7/9)/(4/25+15/25))}}} Add the fractions in the numerator



{{{sqrt((7/9)/(19/25))}}} Add the fractions in the denominator



{{{sqrt((7/9)*(25/19))}}} Flip the second fraction and multiply



{{{sqrt(175/171)}}} Multiply the fractions



Now if you want to evaluate the square root, simply evaluate {{{sqrt(175/171)}}} (or {{{sqrt(1.02339)}}}) to get 



{{{sqrt(175/171)=1.01163}}}