A rectangle has the side lengths root6m and root3m, what is the area of the rectangle in its simplest form.

This question explores surds. To find the area of a rectangle we must multiply its two sides together. When multiplying surds we follow the rule that roota x roota = rootaxa, therefore in this case by multiplying root6 and root3 we get root18, therefore root18m^2 is the area of the rectangle. Now, in order to simplify root18, we must look at the factors of 18, these include 1 and 18, 2 and 9, 3 and 6. Look at these factors and see if any of them have a square number. In this case it is the combination 2 and 9, as 9 is the square of 3. Therefore, the new way of writing root 18 is root9root2 and as we can square root 9 to become 3, then the simplified area of the rectangle is 3root2, therefore the final answer is 3root2m^2.