Radical Calculator
Simplify radicals with prime factorization, step-by-step simplification, and decimal approximations.
Results
Enter values and click Calculate to see the result.
Theory & Formula
What are Radicals?
A radical is the inverse of exponentiation. The nth root of x is the number that, when raised to the nth power, gives x.
Notation
Square Root:
\(\sqrt{x} = x^{1/2}\)Cube Root:
\(\sqrt[3]{x} = x^{1/3}\)nth Root:
\(\sqrt[n]{x} = x^{1/n}\)Simplifying Radicals
To simplify a radical, find perfect nth power factors in the prime factorization and extract them from the radical.
Example:
\(\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}\)Properties
Product Property:
\(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\)Quotient Property:
\(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)