Surd Calculator
Simplify square roots, rationalise denominators and add or subtract surds.
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How to use this calculator
Choose what you want to do. You can simplify a square root, rationalise a denominator of the form a รท (b + cโd), or add and subtract surds.
How it's calculated
โ(a ร b) = โa ร โb, so pull out perfect squares: โ72 = โ(36 ร 2) = 6โ2. To rationalise, multiply top and bottom by the conjugate: (b + cโd)(b โ cโd) = bยฒ โ cยฒd.
Worked example
6 รท (2 + โ3): multiply by (2 โ โ3) รท (2 โ โ3). The bottom is 4 โ 3 = 1, so the answer is 12 โ 6โ3.
Frequently asked questions
What is a surd?
A root that cannot be written as a whole number or simple fraction, like โ2 or โ5.
What is the conjugate?
The same two terms with the sign between them changed: the conjugate of 2 + โ3 is 2 โ โ3.
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Last updated October 2026. Results are for learning and guidance; always check important work. Calculations run in your browser and are not stored.