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Answer:

[tex]=2\sqrt{3}\\\mathrm{Decimal:\quad }\:3.46410[/tex]

Step-by-step explanation:

[tex]\frac{12\sqrt{2}}{2\sqrt{6}}\\\mathrm{Divide\:the\:numbers:}\:\frac{12}{2}=6\\=\frac{6\sqrt{2}}{\sqrt{6}}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a}=a^{\frac{1}{n}}\\\sqrt{6}=6^{\frac{1}{2}}\\=\frac{6\sqrt{2}}{6^{\frac{1}{2}}}\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\frac{6^1}{6^{\frac{1}{2}}}=6^{1-\frac{1}{2}}\\=\sqrt{2}\cdot \:6^{-\frac{1}{2}+1}\\\mathrm{Subtract\:the\:numbers:}\:1-\frac{1}{2}=\frac{1}{2}\\=6^{\frac{1}{2}}\sqrt{2}[/tex]

[tex]\mathrm{Apply\:radical\:rule}:\quad \:a^{\frac{1}{n}}=\sqrt[n]{a}\\6^{\frac{1}{2}}=\sqrt{6}\\=\sqrt{6}\sqrt{2}\\\mathrm{Factor\:integer\:}6=2\cdot \:3\\=\sqrt{2\cdot \:3}\sqrt{2}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}\\\sqrt{2\cdot \:3}=\sqrt{2}\sqrt{3}\\=\sqrt{2}\sqrt{3}\sqrt{2}\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{a}\sqrt{a}=a\\\sqrt{2}\sqrt{2}=2\\=2\sqrt{3}[/tex]

Answer:

[tex]2 \sqrt{3} [/tex]

Step-by-step explanation:

[tex] \frac{ 12\sqrt{2} }{2 \sqrt{6} } [/tex]

Reduce the fraction with 2

[tex] = \frac{6 \sqrt{2} }{ \sqrt{6} } [/tex]

Simplify the expression

[tex] \frac{6}{ \sqrt{3} } [/tex]

Multiply the fraction by [tex] \frac{ \sqrt{3} }{ \sqrt{3} } [/tex]

[tex] \frac{6}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } [/tex]

To multiply the fractions, multiply the numerators and denominators separately

[tex] \frac{6 \sqrt{3} }{ \sqrt{3 \times \sqrt{3} } } [/tex]

When a square root of an expression is multiplied by itself, the result is that expression

[tex] \frac{6 \sqrt{3} }{3} [/tex]

Reduce the fraction with 3

[tex] 2 \sqrt{3} [/tex]

Hope this helps...

Best regards!!

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