In mathematics, a surd is an expression that includes a root, such as a square root, cube root, or any other higher order root, that cannot be simplified to remove the root. Specifically, a surd is typically an irrational number that cannot be expressed as a simple fraction. For example:
- \( \sqrt{2} \) is a surd because it cannot be simplified to a rational number.
- \( \sqrt{4} \) is not a surd because it simplifies to 2, which is a rational number.
Surds are often used in mathematics to maintain precision in calculations involving roots and to express irrational numbers in their original form.
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