In mathematics, a surd is a value in a square root that cannot be further simplified into whole numbers or integers. Surds are irrational numbers. For example, √2, √3, and √5 are surds because they cannot be further simplified. If we further simplify them, we get decimal values. Surds are the square roots of numbers that cannot be simplified into a whole or rational number. In other words, a surd is a root of a whole number that has an irrational value.

There are different types of surds, including simple surds, pure surds, similar surds, mixed surds, compound surds, and binomial surds. Six rules for surds include simplifying surds, rationalizing the denominator, multiplying surds, dividing surds, adding surds, and subtracting surds.

Surd forms arise naturally in a number of applications, such as in the solution of quadratic equations using the formula.