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Posted: September 5th, 2011, 10:49 am

Example 1: $\inline 2\sqrt{3}+3\sqrt{3}$

The radical in each term is the same, so you can combine them. Add the numbers in front of each radical.

$2\sqrt{3}+3\sqrt{3} = (2+3)\sqrt{3}$

= $5\sqrt{3}$

Example 2: $\inline 14\sqrt{20}-3\sqrt{125}$ - The $\inline \sqrt{20}$ has a perfect square in it, $\inline \sqrt{4}$. That leaves 5 under the radical. Same with $\inline \sqrt{125}$; it has a perfect square, $\inline \sqrt{25}$. That also leaves a 5 under the radical

= $\inline 14 \times 2\sqrt{5}-3 \times 5\sqrt{5}$

= $\inline 28\sqrt{5}-15\sqrt{5}$

= $\inline 13\sqrt{5}$