How are squares and square roots related to the triangle?
Squares and square roots are related to triangles through the Pythagorean Theorem. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This relationship can be expressed as a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides of the triangle, and c is the length of the hypotenuse.
The square root is then used to find the length of a side of a right triangle when the lengths of the other two sides are known. For example, if the lengths of the two shorter sides of a right triangle are 3 and 4, the length of the hypotenuse can be found by taking the square root of (3^2 + 4^2) = √(9 + 16) = √25 = 5.