Find the perimeter of a square with a side length of 3square root32
The perimeter of a square is found by multiplying the length of one side by 4. Given that the side length is 3√32, we can substitute this value into the formula to find the perimeter:
Perimeter = 4 * 3√32
To simplify, we can evaluate √32:
√32 = √(16 * 2) = √16 * √2 = 4√2
Now we can substitute this back into the equation:
Perimeter = 4 * 3 * 4√2
Perimeter = 12 * 4√2
Perimeter = 48√2
Therefore, the perimeter of the square with a side length of 3√32 is 48√2.
To find the perimeter of a square, you need to add up the lengths of all four sides.
Given that the side length of the square is 3√32, we can calculate the perimeter by multiplying this length by 4.
Perimeter = 4 * Side Length
Substituting the value of the side length, we get:
Perimeter = 4 * 3√32
Now let's simplify the square root of 32:
√32 = √(16 * 2) = √16 * √2 = 4√2
Replacing this back into the equation:
Perimeter = 4 * 3 * 4√2
Let's simplify this further:
Perimeter = 12 * 4√2
Finally, we multiply 12 by 4√2:
Perimeter = 48√2
Therefore, the perimeter of the square is 48√2.
To find the perimeter of a square with a given side length, we need to multiply the length of one side by 4 since a square has four equal sides.
In this case, the side length is given as 3√32. To simplify this expression, we can break down the number 32 into its prime factors: 32 = 2^5. Taking the square root of 32 becomes the same as taking the square root of 2^5, which simplifies to 2^2√2.
Now, we can substitute the simplified expression for the side length into the perimeter formula:
Perimeter = 4 × side length
Perimeter = 4 × 3√32
Perimeter = 4 × 3 × 2^2√2
Simplifying further, we can multiply the coefficients:
Perimeter = 12 × 2^2√2
Finally, we can simplify 2^2 to get the final answer:
Perimeter = 12 × 4√2
Perimeter = 48√2
Therefore, the perimeter of a square with a side length of 3√32 is 48√2.