Rationalize Denominator Calculator

Your details

Select the structure of your denominator. The calculator picks the right rationalization technique automatically.
The integer or coefficient in your numerator.
The number under the radical sign in the numerator.
The integer coefficient multiplying the radical in the denominator.
The number under the radical sign in the denominator.
Rationalized expression
3√5 / 10

The original fraction rewritten with a rational denominator.

Multiply numerator and denominator by√5/√5
Expanded numerator3√5
Expanded denominator2*√5*√5 = 2*5 = 10
Decimal approximation0.67082
Decimal value0.67082

Denominator rationalized using the monomial square root method.

  • The monomial square root method was used to remove the radical from the denominator.
  • Rationalizing factor applied: √5/√5.
  • Decimal check: the rationalized expression evaluates to approximately 0.670820.

Next stepAlways check your answer by evaluating both the original and rationalized forms numerically - they should match.

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