Rationalize the Denominator – Practice Problems

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An important rule when simplifying radical expressions is that there must be no radical sign in the denominator of the expression. Removing the radical sign in the denominator of an expression is known as rationalizing the denominator.

There are two very important points to remember when rationalizing the denominator. First, the product property of square roots, which states that √a * √b = √ab. This is important when removing a square root of a number, like √a, in the denominator. We can multiply the expression with a fraction equal to one, like √b/√b, so that the denominator product √ab can be simplified, if ab is a perfect square.

Second, the conjugate, which can be obtained by multiplying the second term of a binomial by -1. This is what we use when we have a term, like (a + √b) in the denominator. We multiply the expression with a fraction equal to 1, specifically (a - √b)/(a - √b), so that after multiplying, we will have a^2 + a√b - a√b - √(b^2), where the middle terms cancel each other out.

You will definitely find that rationalizing the denominator is an easy tool in simplifying expressions, especially when you master these two points.

Expressions and Equations Work with radicals and integer exponents.

CCSS.MATH.CONTENT.8.EE.A.2

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Exercises in this Practice Problem
Simplify $\frac{2}{\sqrt3}$ as well as $\frac2{4\sqrt3}$.
Determine the steps for simplifying $\frac3{5-\sqrt7}$.
Find the right factor to simplify the fraction.
Calculate the ratios.
Define the conjugate of $a+b$ and its use.
Simplify the given fractions.