Rationalize the Denominator Calculator

How to Rationalize The Denominator And Simplify?

In terms of rationalizing denominators with radicals, below are the four opportunities, and those also are used by our rationalize the denominator calculator.

Radical/Radical ((a * ⁿ√b) / (x * ᵏ√y)):

• Multiply the given expression with the term beneath:

ᵏ√(y^ᵏ⁻¹) / ᵏ√(y^ᵏ⁻¹)

• by using locating the product, you will get the solution within the form:

x * ᵏ√y * ᵏ√(y^ᵏ⁻¹)

= x * ᵏ√(y^ᵏ)

= x * y

That is the most easy case that this rationalize denominator calculator works on to generate accurate outcomes.

Sum/Radical ((a * ⁿ√b + c * ᵐ√d) / (x * ᵏ√y)):

• locate the manufactured from the given term with the ᵏ√(y^ᵏ⁻¹) / ᵏ√(y^ᵏ⁻¹) as same for the first case
• After that, the most essential component that this calculator considers for accurate calculations is a made of the amount ᵏ√(y^ᵏ⁻¹) with both numerator monomials one by one

Radical/Sum ((a * √b) / (x * √y + z * √u)):

This is in which the real technicality starts!

• cross by using multiplying the denominator terms with (x * √y - z * √u) / (x * √y - z * √u)
• After that, you need to try to get the simplified time period within the form of the following formula:

(a - b) * (a + b) = a^2 - b^2

• This may lead you to get the simplification of the rationalizing denominators within the final shape inside the denominator as follows:

x^2 - y^2

Sum/Sum ((a * √b + c * √d) / (x * √y + z * √u)):

As we are coping with the guide formulas here, so that you need to multiply each the quantities in the numerator through the subsequent expression one after the other:

(x * √y - z * √u ) /(x * √y - z * √u)

A way to Rationalize the Denominator?

Allow’s resolve an instance to clarify your idea regarding rationalizing denominators!

Example :

How do you rationalize a denominator given as follows:

$$ \frac{2 * \sqrt{3}}{5 * \sqrt{8}} $$

Solution:

Here we have:

$$ \frac{2 * \sqrt{3}}{5 * \sqrt{8}} $$

$$ \frac{2 * \sqrt{3}}{5 * \sqrt{4 * 2}} $$

$$ \frac{2 * \sqrt{3}}{5 * \sqrt{2^{2} * 2}} $$

$$ \frac{2 * \sqrt{3}}{5 * 2 * \sqrt{2}} $$

$$ \frac{2 * \sqrt{3}}{10 * \sqrt{2}} $$

To rationalize the denominator, multiply numerator and denominator with the aid of \( \sqrt{2} \):

$$ \frac{2 * \sqrt{3} * \sqrt{2}}{10 * \sqrt{2} * \sqrt{2}} $$

$$ \frac{2 * \sqrt{6}}{10 * 2} $$

$$ \frac{\sqrt{6}}{10} $$

$$ 0.1 * \sqrt{6} $$

That is the specified solution that also can be verified via the use of a rationalize denominator calculator.

Faqs:

Ought to You usually Rationalize The Denominator?

No, of route not! Rationalizing is handiest accomplished while you are caught with complicated calculations and there seems no method to simplify the hassle.