Rewrite a / (c√d) with no radical in the denominator
a =
c =
d =
Result
Rationalized Form
Step-by-Step Derivation
Rationalize Denominator Formula
a/(c√d) × √d/√d = a√d/(cd)
Rationalizing a denominator removes the square root from the bottom of a fraction. Multiplying by √d/√d keeps the value unchanged while turning c√d into cd, which is easier to compare and simplify.
⚠Note: This page handles simple monomial radical denominators c√d with nonnegative integer d. The denominator cannot equal zero.
How Rationalizing Works
Multiply the numerator and denominator by the same radical factor, then simplify the new denominator and reduce the coefficient fraction.
Same Factor
Use √d over √d so the fraction value does not change.
No Radical Bottom
√d · √d becomes d in the denominator.
Reduce Fraction
Common numeric factors can be simplified afterward.
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