#color(blue)("Assumption: you really meant the question to be as written")#
#color(brown)("3sqrt(5)xxsqrt(5)+3sqrt(5)xx2sqrt(75)#
As you there is no grouping by brackets we have to look at priority of action (add, divide, multiply etc). Multiplication has a higher priority than add so we have to apply that first. Thus we have:
#(3sqrt(5)xxsqrt(5))+(3sqrt5xx2sqrt(75))#
#(3xx(sqrt(5))^2)+(3xx2xxsqrt(5)xxsqrt(75))#
note that #75->5xx15# so #sqrt(5)xxsqrt(75)->(sqrt(5))^2xxsqrt(15)#
#(3xx(sqrt(5))^2)+(3xx2xx(sqrt(5))^2xxsqrt(15))#
#color(white)("dddd")(15)color(white)("ddd")+color(white)("ddd")(30+sqrt(15))#
#45+sqrt(15)#
Note that #15=3xx5# and both 3 and 5 prime numbers so it is simpler to leave the #sqrt(15)# as it is.
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#color(blue)("Assumption: the brackets are the wrong way round")#
Having the brackets round the way you have is very unexpected.
#color(brown)( (3sqrt(5))xx(sqrt(5)+3sqrt(5))xx(2sqrt(5)))#
#(3sqrt(5))xxcolor(white)("dd")(4sqrt(5))color(white)("ddd")xx(2sqrt(5))#
Dealing with the whole numbers part #->3xx4xx2=color(red)(24)#
Dealing with the square roots part #color(white)("d")->(sqrt(5)xxsqrt(5))xxsqrt5#
#color(white)("dddddddddddddddddddddddddd")->color(white)("dddd") 5color(white)("dddd")xxsqrt(5)=color(purple)(5sqrt(5))#
Putting it all together we have: #color(red)(24)color(purple)(xx5sqrt(5)) = 120sqrt(5)#
