Answer:
- [tex]3\sqrt{6}\times \:2\sqrt{3}=18\sqrt{2}[/tex]
- [tex]5\sqrt{12}+3\sqrt{3}=13\sqrt{3}[/tex]
Step-by-step explanation:
1)
Given the expression
[tex]3\sqrt{6}\:\times \:2\sqrt{3}[/tex]
[tex]\mathrm{Factor\:integer\:}6=3\times \:2[/tex]
[tex]=3\sqrt{3\times \:2}\times \:2\sqrt{3}[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}[/tex]
[tex]=3\sqrt{3}\sqrt{2}\times \:2\sqrt{3}[/tex]
[tex]\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{a}=a[/tex]
[tex]=3\times \:2\times \:3\sqrt{2}[/tex]
[tex]=18\sqrt{2}[/tex]
Thus,
[tex]3\sqrt{6}\times \:2\sqrt{3}=18\sqrt{2}[/tex]
2)
Given the expression
[tex]5\sqrt{12}+3\sqrt{3}[/tex]
[tex]\:=\:5\sqrt{\left(4\right)\left(3\right)}+3\sqrt{3}[/tex]
[tex]=\:5\times 2\sqrt{\left(3\right)}+3\sqrt{3}[/tex]
[tex]=10\sqrt{3}+3\sqrt{3}[/tex]
[tex]\mathrm{Add\:similar\:elements:}\:10\sqrt{3}+3\sqrt{3}=13\sqrt{3}[/tex]
[tex]=13\sqrt{3}[/tex]
Thus,
[tex]5\sqrt{12}+3\sqrt{3}=13\sqrt{3}[/tex]
