How to Use Denominator Rationalization Calculator
Denominator Rationalization Calculator accepts simple fraction expressions with square-root denominators. Enter examples such as 1/sqrt(2), 3/(2+sqrt(5)), or sqrt(3)/(sqrt(6)-sqrt(2)). Denominator Rationalization Calculator identifies the denominator pattern, selects a factor, and displays the rationalized form.
The result area shows the multiplication factor, the denominator after multiplication, and whether a single radical factor or conjugate factor was used.
Formula & Theory — Denominator Rationalization Calculator
Denominator Rationalization Calculator relies on equivalent fractions:
a / b = (a x c) / (b x c)
For a single square root, the factor is the same radical. For example, multiplying by sqrt(a) turns sqrt(a) into a. For a binomial denominator such as p + sqrt(q), Denominator Rationalization Calculator uses the conjugate p - sqrt(q), because (p + sqrt(q))(p - sqrt(q)) = p^2 - q.
Use Cases for Denominator Rationalization Calculator
Denominator Rationalization Calculator is useful for algebra practice, radical simplification, homework checking, and teaching conjugates. Students can use Denominator Rationalization Calculator to see why a denominator becomes rational. Teachers can use Denominator Rationalization Calculator to compare single radical and binomial radical cases. The tool is intentionally focused on readable intermediate steps rather than hiding everything inside a symbolic algebra engine.