Write a radical for exact length of the diagonal of the 30 by 30 dance floor. simplify the radical.
Im not sure how to do this.
What is Pythagorean theorem?
since it's 30 by 30, the shape is a square.
recall that the diagonal of a square is given by:
diagonal = sqrt(s)
where s = length of a side
thus, the diagonal is
sqrt(30)
hope this helps~ :)
To find the exact length of the diagonal of a square dance floor, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In the case of a square dance floor, the two sides are equal (each side equal to 30 units). So, we can consider the diagonal as the hypotenuse of a right triangle formed by two sides of the square.
To find the length of the diagonal, we can use the formula:
diagonal^2 = side^2 + side^2
diagonal^2 = 30^2 + 30^2
diagonal^2 = 900 + 900
diagonal^2 = 1800
Now, we can simplify the radical by finding the square root of both sides:
diagonal = √1800
To simplify the radical, we look for perfect square factors of 1800. In this case, 1800 can be factored as 900 x 2. Since 900 is a perfect square (30^2), we can simplify the radical further:
diagonal = √(900 x 2)
diagonal = √900 x √2
diagonal = 30√2
Therefore, the exact length of the diagonal of the 30 by 30 dance floor is 30√2 units.