Respuesta :

sqdancefan

1. You need to multiply the denominator by something that will make the content of the radical be a square—so that when you take the square root, you get something rational. Easiest and best is to multiply by √6. Of course, you must multiply the numerator by the same thing. Then simplify.

[tex]\displaystyle\frac{2}{\sqrt{6}}=\frac{2}{\sqrt{6}}\cdot\frac{\sqrt{6}}{\sqrt{6}}\\\\=\frac{2\sqrt{6}}{\sqrt{6}\cdot\sqrt{6}}=\frac{2\sqrt{6}}{6}\\\\=\bf{\frac{\sqrt{6}}{3}}[/tex]

2. Identify the squares under the radical and remove them.

[tex]5\sqrt{12xm^3}=5\sqrt{(4m^2)(3xm)}=5\sqrt{(2m)^2}\sqrt{3xm}\\\\=5\cdot 2m\sqrt{3xm}=\bf{10m\sqrt{3xm}}[/tex]

tramserran

Rationalize means to eliminate the radical (square root) from the denominator.

[tex]\frac{2}{\sqrt{6}} * \frac{\sqrt{6}}{\sqrt{6}} = \frac{2\sqrt{6} }{6} = \frac{\sqrt{6}}{3}[/tex]

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Simplify means to move the "groups" from inside the radical to outside the radical.

 5[tex]\sqrt{12xm^{3} }[/tex]

= 5[tex]\sqrt{2 * 2 * 3 * x * m * m * m }[/tex]

= 5[tex]\sqrt{(2 * 2) * 3 * x * m * (m * m) }[/tex]

= 5 * 2 * m[tex]\sqrt{3 * x * m}[/tex]

= 10m[tex]\sqrt{3xm}[/tex]

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