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Math Calculators ▶ Rationalize the Denominator Calculator

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**Table of Content**

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.

- Multiply the given expression with the term below:

**ᵏ√(y^ᵏ⁻¹) / ᵏ√(y^ᵏ⁻¹)**

- By finding the product, you will get the answer in the form:

**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.

- Find the product of the given term with the
**ᵏ√(y^ᵏ⁻¹) / ᵏ√(y^ᵏ⁻¹)**as same for the first case - After that, the most important factor that this calculator considers for accurate calculations is a product of the quantity ᵏ√(y^ᵏ⁻¹) with both numerator monomials separately

This is where the actual technicality begins!

- Go by multiplying the denominator terms with
**(x * √y – z * √u) / (x * √y – z * √u)** - After that, you should strive to get the simplified term in the form of the following formula:

**(a – b) * (a + b) = a^2 – b^2**

- This will lead you to get the simplification of the rationalizing denominators in the final form in the denominator as follows:

**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:**

- First of all, select the mode i.e; “
**Simple**” or “**Advanced**”

**If You Select Simple Mode:**

- Select the expression from the drop-down list
- Now enter the required parameters of the expressions in their designated fields
- Tap Calculate

**If You Select Advanced Mode:**

- Enter the numerator and denominator expressions
- Tap Calculate

**Output:**

- Rationalization of denominators
- Step-by-step calculations

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