Question

NEED URGENT HELP!! WILL GIVE BRAINLIEST

Answer 1

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.

$\displaystyle\frac{2}{\sqrt{6}}=\frac{2}{\sqrt{6}}\cdot\frac{\sqrt{6}}{\sqrt{6}}\\\\=\frac{2\sqrt{6}}{\sqrt{6}\cdot\sqrt{6}}=\frac{2\sqrt{6}}{6}\\\\=\bf{\frac{\sqrt{6}}{3}}$

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

$5\sqrt{12xm^3}=5\sqrt{(4m^2)(3xm)}=5\sqrt{(2m)^2}\sqrt{3xm}\\\\=5\cdot 2m\sqrt{3xm}=\bf{10m\sqrt{3xm}}$

Answer 2

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

$\frac{2}{\sqrt{6}} * \frac{\sqrt{6}}{\sqrt{6}} = \frac{2\sqrt{6} }{6} = \frac{\sqrt{6}}{3}$

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

 5$\sqrt{12xm^{3} }$

= 5$\sqrt{2 * 2 * 3 * x * m * m * m }$

= 5$\sqrt{(2 * 2) * 3 * x * m * (m * m) }$

= 5 * 2 * m$\sqrt{3 * x * m}$

= 10m$\sqrt{3xm}$