The square root of a number is a value that, when multiplied by itself, gives the original number. The square root of 9 is 3 because 3 × 3 = 9. The symbol √ is called a radical. Every positive number has two square roots: one positive and one negative.

Perfect squares have integer square roots: 1, 4, 9, 16, 25, and so on. Other numbers have irrational square roots, like √2. The square root of a negative number is imaginary in the real number system, but becomes a complex number using i.

Square roots appear in geometry (Pythagorean theorem), physics (root mean square), and statistics (standard deviation). Calculating them by hand uses methods like Newton's approximation. Calculators and computers handle them instantly, but understanding the concept remains essential.

• Value that squares to a given number
• Positive numbers have two roots
• Perfect squares have integer roots
• Used in geometry, physics, and statistics