Find the perimeter of the figure below. Show all work for each step. Work should include explanations in words detailing how you simplify each specific radical. Take your time and be thorough. Include units in final answer.
2√6
3√54
To find the perimeter, we need to add up the lengths of all the sides.
For the first side, we have 2√6. This is already in simplest form.
For the second side, we have 3√54. We can simplify this by factoring out a perfect square from the inside of the radical:
3√54 = 3√(9*6) = 3√9 * √6 = 3 * 3√6 = 9√6
Now we can add up the lengths of both sides:
2√6 + 9√6 = 11√6
So the perimeter of the figure is 11√6, or approximately 23.80 units.