Radical Simplifier - √ Cube Root, nth Root Calculator | 8gwifi.org

Radical Simplifier

Simplify square roots, cube roots, nth roots with rationalization and operations

Radical Calculator
Simplify radicals:
Enter the radicand (number under the radical) and the index (root type: 2 for √, 3 for ∛)
Must be non-negative
Examples:
√72 = 6√2 (72 = 36 × 2)
∛54 = 3∛2 (54 = 27 × 2)
√50 = 5√2 (50 = 25 × 2)
Radical operations:
Multiply, divide, add, or subtract radicals
Examples:
√12 × √6 = √72 = 6√2
√50 ÷ √2 = √25 = 5
3√5 + 2√5 = 5√5
7√3 - 4√3 = 3√3
Rationalize denominators:
Remove radicals from denominators by multiplying by conjugates
Examples:
5/√3 = (5√3)/3
√8/√2 = 2
1/(2 + √3) = (2 - √3)/(4 - 3) = 2 - √3
Simplify nested radicals:
Simplify expressions like √(a + √b) or √(a - √b)
Example:
√(7 + √40) = √5 + √2
Verification: (√5 + √2)² = 5 + 2√10 + 2 = 7 + 2√10 = 7 + √40 ✓
Understanding Radicals
What is a Radical?

A radical (√) represents the root of a number. The most common is the square root, but cube roots and higher roots are also radicals.

n√a where n is the index and a is the radicand
Simplification Rules

1. Product Property:

√(ab) = √a × √b

2. Quotient Property:

√(a/b) = √a / √b

3. Simplification Process:

  • Factor the radicand into perfect squares (or cubes for ∛)
  • Take the root of perfect powers
  • Leave remaining factors under the radical

4. Adding/Subtracting:

a√c + b√c = (a + b)√c (like radicals only)

5. Rationalizing:

Multiply numerator and denominator by the radical to eliminate it from the denominator.

a/√b = (a√b)/(√b × √b) = (a√b)/b
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