Odpowiedź:
6√18=6√(9*2)=18√2 √35*√21=√(35*21)=√( 5*7*7*3)=√(7²*15)=7√15
3/4 √20=3/4√(4*5)=3/2 √5
2√8*√27=2√( 4*2)*√(9*3)= 4√2*3√3=12√6
Szczegółowe wyjaśnienie:
[tex]a)\ \ 6\sqrt{18}=6\sqrt{9\cdot2}=6\cdot3\sqrt{2}=18\sqrt{2}\\\\b)\ \ \frac{3}{4}\sqrt{20}=\frac{3}{4}\sqrt{4\cdot5}=\frac{3}{\not4_{2}}\cdot\not2^1\sqrt{5}=\frac{3}{2}\sqrt{5}\\\\c)\ \ \sqrt{35}\cdot\sqrt{21}=\sqrt{35\cdot21}=\sqrt{735}=\sqrt{49\cdot15}=\sqrt{49}\cdot\sqrt{15}=7\sqrt{15}\\\\d)\ \ 2\sqrt{8}\cdot\sqrt{27}=2\sqrt{4\cdot2}\cdot\sqrt{9\cdot3}=2\cdot2\sqrt{2}\cdot3\sqrt{3}=4\sqrt{2}\cdot3\sqrt{3}=12\sqrt{6}[/tex]
