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Sagot :

Answer: Hello, my name is woods 245. And I'm here to answer your question.

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Step-by-step explanation:

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.