A square root is a fundamental mathematical concept. It represents a number that, when multiplied by itself, gives us the original number. For example, the square root of 16 is 4, because 4 times 4 equals 16.
We use the radical symbol, written as the square root sign, to denote square roots. When we write the square root of a equals x, it means that x squared equals a. For example, the square root of 9 equals 3, because 3 squared equals 9.
An important property of square roots is that every positive number actually has two square roots: one positive and one negative. For example, both positive 5 and negative 5 are square roots of 25, because both when squared give 25. However, when we write the square root symbol, we typically mean the principal or positive root. Zero is special - it has only one square root, which is zero itself.
It's helpful to memorize the square roots of perfect squares. These are numbers whose square roots are whole numbers. Starting from 1: the square root of 1 is 1, square root of 4 is 2, square root of 9 is 3, and so on up to the square root of 100 which is 10. Knowing these common square roots will help you solve problems more quickly.
Square roots have many practical applications. They're essential in geometry, especially with the Pythagorean theorem, where we find the hypotenuse of a right triangle. They're also used in physics for distance calculations, engineering problems, and statistics. Remember the key properties: the square root of x squared equals the absolute value of x, and square roots can be multiplied and divided following specific rules. Understanding square roots is fundamental for advanced mathematics.