How to Calculate Radicals & Roots
What is Radicals & Roots?
A radical expression contains a root symbol (√). The nth root of x: ⁿ√x = x^(1/n). Square roots (n=2) are most common. Simplifying radicals means removing perfect square factors from inside the radical.
Step-by-Step Guide
- 1√(ab) = √a × √b (product rule for radicals)
- 2√(a/b) = √a / √b (quotient rule)
- 3Simplify: √72 = √(36×2) = 6√2
- 4Rationalize denominator: 1/√2 = √2/2
Worked Examples
Input
√48
Result
4√3
√(16×3) = 4√3
Input
∛(54)
Result
3∛2
∛(27×2) = 3∛2
Input
√(x²y⁴)
Result
xy²
Assuming x,y ≥ 0
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