Mathematics July 22, 2026 · 9 min read

Dividing Radicals: Simplifying Radical Fractions

Learn to divide and simplify radical expressions. Rationalize denominators and work with square roots, cube roots, and higher radicals.

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Dividing radicals involves applying the quotient rule for radicals and rationalizing the denominator. These skills are essential for simplifying expressions in algebra and calculus.

The Quotient Rule

√a ÷ √b = √(a/b)

Rationalizing

To remove a radical from the denominator, multiply both numerator and denominator by the radical:

√a/√b × √b/√b = √(ab)/b

Worked Example

Divide √50 ÷ √2:

  1. √50 ÷ √2 = √(50/2) = √25 = 5
  2. Result: 5