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.

217. 82/3

218. 163/4

219. 274/3

220. 95/2

221. 645/6

222. 1252/3

223. 1000−2/3

224. 32−1/5

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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.

235. 610/3 · 61/3

236. 53/4 · 515/4

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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: image ≈ 1.4, image ≈ 1.7, image ≈ 2.2

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