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Chapter 5

Raking in Radicals

Radical expressions are characterized by radical symbols and an index — a small number written in front of the radical symbol that indicates whether you have a cube root, a fourth root, and so on. When no number is written in front of the radical, you assume it’s a square root.

The Problems You’ll Work On

In this chapter, you get plenty of practice working with radicals in the following ways:

 Simplifying radical expressions by finding a perfect square factor

 Rationalizing denominators with one term

 Rationalizing denominators with two terms, using a conjugate

 Rewriting radicals with fractional exponents

 Dividing with radicals

 Solving operations involving fractional exponents

 Estimating the values of radical expressions

What to Watch Out For

As you get in your groove, solving one radical problem after another, don’t overlook the following:

 Choosing the largest perfect square factor when simplifying a radical expression

 Multiplying correctly when writing equivalent fractions, using conjugates

 Performing operations correctly when fractions are involved

 Checking radical value estimates by comparing to nearest perfect square values

Simplifying Radical Expressions

191–196 Simplify the radical expressions.

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Rationalizing Denominators

197–210 Simplify the fractions by rationalizing the denominators.

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Using Fractional Exponents for Radicals

211–216 Rewrite each radical expression using a fractional exponent.

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Evaluating Expressions with Fractional Exponents

217–226 Compute the value of each expression.

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Operating on Radicals

227–234 Perform the operations on the radicals.

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Operating on Factors with Fractional Exponents

235–242 Perform the operations on the expressions.

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Estimating Values of Radicals

243–250 Estimate the value of the radicals to the nearer tenth after simplifying the radicals. Use:

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