Final answer:
The area of a rectangle with length 3√6 and width 5√2 is calculated as 30√3 square units after multiplying the dimensions and simplifying the square root.
Step-by-step explanation:
To find the area of a rectangle, we use the formula
area = length × width.
In this case, the length of the rectangle is given as 3√6 and the width as 5√2.
We multiply these two values to compute the area:
Area = (3√6) × (5√2) = (3×5)×(√6×√2) = 15√12
Since √12 can be simplified to 2√3 (because 12 = 4 × 3 and √4 = 2), we get:
Area = 15 × 2√3 = 30√3 square units.