Question 752286
Assume the problem is:
{{{1/2}}}{{{sqrt(5)}}} + 1 {{{1/2}}}{{{sqrt(20)}}} = {{{7/2}}}{{{sqrt(5)}}}
Make the 1 and 1/2 an improper fraction
{{{1/2}}}{{{sqrt(5)}}} + {{{3/2}}}{{{sqrt(20)}}} = {{{7/2}}}{{{sqrt(5)}}} 
multiply the equation by 2, this gets rid of the denominators
{{{sqrt(5)}}} + {{{3*sqrt(20)}}} = {{{7*sqrt(5)}}}
Factor inside the middle radical to reveal a perfect square
{{{sqrt(5)}}} + {{{3*sqrt(4*5)}}} = {{{7*sqrt(5)}}}
Extract the square root of 4
{{{sqrt(5)}}} + {{{3*2*sqrt(5)}}} = {{{7*sqrt(5)}}} 
{{{sqrt(5)}}} + {{{6*sqrt(5)}}} = {{{7*sqrt(5)}}}
they are like terms now sqrt(5) just add
{{{7*sqrt(5)}}} = {{{7*sqrt(5)}}} which is obviously true