Answer:
[tex]3+\sqrt{3}[/tex] , [tex]5\sqrt{5}[/tex], [tex]2\sqrt{2}[/tex], and [tex]18 -2\sqrt{2}[/tex]
Step-by-Step Explanation:
1)
[tex]\sqrt{3}(\sqrt{3}+1)[/tex]
Distribute the square root:
[tex]\sqrt{9}+\sqrt{3}[/tex]
[tex]3+\sqrt{3}[/tex]
2)
[tex](\sqrt{5} )(\sqrt{5} )(\sqrt{5} )[/tex]
[tex]\sqrt{(5)(5)(5)}[/tex]
[tex]\sqrt{(25)(5)}[/tex]
[tex](\sqrt{25}) (\sqrt{5)}[/tex]
[tex]5\sqrt{5}[/tex]
3)
[tex](\sqrt{2} )(\sqrt{2} )(\sqrt{2} )[/tex]
[tex]\sqrt{(2)(2)(2)}[/tex]
[tex]\sqrt{(4)(2)}[/tex]
[tex](\sqrt{4}) (\sqrt{2)}[/tex]
[tex]2\sqrt{2}[/tex]
4)
[tex](3\sqrt{2})^{2} -2\sqrt{2}[/tex]
[tex](9)(2) -2\sqrt{2}[/tex]
[tex]18 -2\sqrt{2}[/tex]
If you need it factored:
[tex]2(9-\sqrt{2})[/tex]
Keep in mind that square roots can be positive or negative.
