√75+√18⋅√27 Note: When simplifying surds, express the surd as a product of a perfect square and a number 22=4 and √4=2 32=9 and √9=3 42=16 and √16=4 52=25 and √25=5 62=36 and √36=6 72=49 and √49=7 82=64 and √64=8 92=81 and √81=9 102=100 and √100=10 112=121 and √121=11 122=144 and √144=12 132=169 and √169=13 142=196 and √196=14 152=225 and √225=15 75=25×3 18=9×2 27=9×3 √75+√18⋅√27=√25×3+√9×2⋅√9×3 √a×b=√a×√b √75+√18⋅√27=√25×√3+√9×√2−√9×√3 √25=5 √9=3 √75+√18−√27=5√3+3√2−3√3 √75+√18⋅√27=5√3−3√3+3√2 √75+√18−√27=2√3+3√2