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Pearson Algebra 1 Common Core, 2011

PA

Pearson Algebra 1 Common Core, 2011 View details

2. Simplifying Radicals

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Exercise 79 Page 625

The Multiplication Property of Square Roots tells us that sqrt(ab)=sqrt(a) * sqrt(b), for a≥ 0 and b≥ 0.

C

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that y≥0, otherwise the given expression would not be defined. sqrt(12y^5)Let's recall the Multiplication Property of Square Roots. sqrt(ab)=sqrt(a) * sqrt(b), for a≥ 0,b≥ 0 Let's use this property for our expression.

sqrt(12y^5)

SplitIntoFactors

Split into factors

sqrt(4* 3y* y^2* y^2)

sqrt(a* b)=sqrt(a)*sqrt(b)

sqrt(4)sqrt(3y)sqrt(y^2)sqrt(y^2)

▼

Simplify factors

Calculate root

2sqrt(3y)sqrt(y^2)sqrt(y^2)

SqrtPowToNumber

sqrt(a^2)=a

2sqrt(3y)y* y

ProdToPowTwoFac

a* a=a^2

2sqrt(3y)y^2

CommutativePropMult

Commutative Property of Multiplication

2y^2sqrt(3y)

The simplified form of the given expression is 2y^2sqrt(3y), which corresponds to answer C.

Subchapter links

Lesson Check p.623

Practice and Problem-Solving Exercises p.623-625

Standardized Test Prep p.625

Mixed Review p.625