Mastering Perfect Squares

A perfect square is a number that can be expressed as the product of two equal integers. For example, $4$ is a perfect square because it can be expressed as $2 \cdot 2$.

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of $9$ is $3$ because $3 \cdot 3 = 9$.

The Pythagorean theorem can be applied to solve problems involving right triangles. It states that 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. The equation can be written as $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs of the triangle and $c$ is the length of the hypotenuse.