Calculate Square Perimeter: Solving (√3·√12-5)²·3² Side Length Problem

To calculate the perimeter of a square, we need to first determine the length of one side and then use the formula for the perimeter of a square, which is given by $4 \times \text{side length}$.

The side length is given as $(\sqrt{3}\cdot\sqrt{12}-5)^2\cdot3^2$. Let's simplify this expression step by step:

• First, simplify the square roots: $\sqrt{3}$ and $\sqrt{12}$.

  • $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4}\times \sqrt{3} = 2 \times \sqrt{3}$
  • Thus, $\sqrt{3} \times \sqrt{12} = \sqrt{3} \times 2 \times \sqrt{3} = 2 \times 3 = 6$.
• Next, substitute back into the expression: $(6 - 5)^2 \cdot 3^2$.
• Simplify inside the parentheses: $6 - 5 = 1$, so we have $1^2 \cdot 3^2$.
• Calculate the squares: $1^2 = 1$ and $3^2 = 9$.
• Multiply the results: $1 \times 9 = 9$.

The side length of the square is therefore $9$.

Thus, the perimeter of the square is:

• $4 \times 9 = 36$.

Therefore, the perimeter of the square is $36$.