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Pearson Algebra 2 Common Core, 2011

PA

Pearson Algebra 2 Common Core, 2011 View details

5. Solving Square Root and Other Radical Equations

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Exercise 83 Page 397

Start by converting the decimal in the exponent to a fraction. Then rewrite the base as a product involving perfect $n^{th}$ factors where $n$ is the denominator of the exponent.

$125$

Practice makes perfect

We want to simplify the given number. Let's start by converting the decimal in the exponent to a fraction.

2 5^{1.5} \Leftrightarrow 2 5^{\frac{3}{2}}

We will split the base into perfect square factors to simplify this fraction. Because the denominator of the exponent is

2,

this will allow us to simplify the rational exponent.

2 5^{\frac{3}{2}}

SplitIntoFactors

Split into factors

(5 \cdot 5)^{\frac{3}{2}}

ProdToPowTwoFac

$a \cdot a = a^{2}$

(5^{2})^{\frac{3}{2}}

$(a^{m})^{n} = a^{m \cdot n}$

5^{2 \cdot \frac{3}{2}}

DenomMultFracToNumber

$2 \cdot \frac{a}{2} = a$

5^{3}

Calculate power

125

Subchapter links

Lesson Check p.394

Practice and Problem-Solving Exercises p.395-397

Standardized Test Prep p.397