Simplify radical expression

Simplify radical expression

Postby Guest » Tue Jan 29, 2019 4:55 am

[tex]\frac{3\sqrt{3}+\sqrt{6}}{\sqrt{6}-\sqrt{2}*2\sqrt{3}+3}[/tex]
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Re: Simplify radical expression

Postby nathi123 » Tue Jan 29, 2019 7:36 am

A=[tex]\frac{3\sqrt{3}+\sqrt{6}}{\sqrt{6}-2\sqrt{6}+3}=\frac{\sqrt{3}(3+\sqrt{2)}}{3-\sqrt{6}}=\frac{\sqrt{3}(3+\sqrt{2)}}{\sqrt{3}(\sqrt{3}-\sqrt{2})}[/tex]
because [tex]\sqrt{2}*2\sqrt{3}=2\sqrt{2}.\sqrt{3}=2\sqrt{6} ; 3=(\sqrt{3})^{2}[/tex]
[tex]\Rightarrow A=\frac{3+\sqrt{2}}{\sqrt{3}-\sqrt{2}}.\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}=3\sqrt{3}+3\sqrt{2}+\sqrt{6}+2[/tex].

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Re: Simplify radical expression

Postby marthasimons » Tue Feb 18, 2020 5:19 am

WOW cool

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Re: Simplify radical expression

Postby HallsofIvy » Tue Feb 18, 2020 9:15 am

Did you not, yourself, at least notice that [tex]\sqrt{2}*2\sqrt{3}= 2\sqrt{6}[/tex], so that [tex]\sqrt{6}- \sqrt{2}*2\sqrt{3}= -\sqrt{6}[/tex]?

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