Radical Calculator
Simplify radicals, square roots, and cube roots instantly with step-by-step solutions
Simplify Radicals
How it works:
Find the largest perfect square (or cube) that divides the radicand, then simplify by extracting the root.
Example: 72
Simplified Form:
Frequently Asked Questions
How do you simplify radicals?
To simplify a radical, find the largest perfect square (for square roots) that divides the radicand, then rewrite as a product. Extract the square root of the perfect square factor. For example, √72 = √(36 × 2) = 6√2.
What is a radicand?
The radicand is the number or expression under the radical symbol (√). In √25, the radicand is 25. In √(x + 3), the radicand is (x + 3).
Can you add radicals?
You can only add radicals with the same radicand and index (like radicals). For example, 2√3 + 5√3 = 7√3, but √2 + √3 cannot be simplified further because they have different radicands.
What are perfect squares?
Perfect squares are numbers that result from squaring an integer: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc. They're essential for simplifying square roots because their square roots are whole numbers.
How do you multiply radicals?
To multiply radicals with the same index, multiply the radicands and keep the radical: √a × √b = √(ab). For example, √3 × √12 = √36 = 6. Always simplify your final answer.
What is rationalizing the denominator?
Rationalizing means eliminating radicals from the denominator of a fraction. Multiply both numerator and denominator by a radical that eliminates the radical in the denominator. For 1/√2, multiply by √2/√2 to get √2/2.