Math Calculators ▶ Rationalize the Denominator Calculator
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Our rationalize the denominator calculator helps you rationalize the denominators containing radicals. Moreover, the tool can also rationalize expressions with complex square root terms as well.
When it comes to rationalizing denominators with radicals, below are the four possibilities, and these are also used by our rationalize the denominator calculator.
ᵏ√(y^ᵏ⁻¹) / ᵏ√(y^ᵏ⁻¹)
x * ᵏ√y * ᵏ√(y^ᵏ⁻¹)
= x * ᵏ√(y^ᵏ)
= x * y
This is the most simple case that this rationalize denominator calculator works on to generate accurate results.
This is where the actual technicality begins!
(a – b) * (a + b) = a^2 – b^2
x^2 – y^2
As we are coping with the manual formulas here, so you need to multiply both the quantities in the numerator by the following
expression separately:
(x * √y – z * √u ) /(x * √y – z * √u)
Let’s resolve an example to clarify your concept regarding rationalizing denominators!
How do you rationalize a denominator given as under:
$$ \frac{3 * \sqrt{5}}{4 * \sqrt{16}} $$
Here we have
$$ \frac{3 * \sqrt{5}}{4 * \sqrt{16}} $$
$$ \frac{3 * \sqrt{5}}{4 * \sqrt{4*4}} $$
$$ \frac{3 * \sqrt{5}}{4 * \sqrt{4^{2}}} $$
$$ \frac{3 * \sqrt{5}}{4 * 4} $$
$$ \frac{3 * \sqrt{5}}{16} $$
$$ 0.1875 * \sqrt{5} $$
This is the required answer that can also be verified by this rationalize denominator calculator.
The rationalize calculator is loaded with a simple user-interface that lets you enter a few inputs to get instant rationalization of the
denominators.
Input:
If You Select Simple Mode:
If You Select Advanced Mode:
Output:
No, of course not! Rationalizing is only done when you are stuck with complicated calculations and there seems no solution to simplify the problem.
To rationalize the given denominator, go by multiplying the expression with √7/√7 such that:
1/√7 x √7/√7
= √7
From the source Wikipedia: Rationalisation (mathematics), Rationalisation of a monomial square root and cube root, Dealing with more square roots, Generalizations
From the source Lumen Learning: Rationalize Denominators, One Term, Two Terms