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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

2. Simplifying Radicals

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Exercise 75 Page 625

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

10b^2

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that b≥0, otherwise the given expression would not be defined. 2b(sqrt(5b))^2 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.

2b(sqrt(5b))^2

SplitIntoFactors

Split into factors

2b(sqrt(5* b))^2

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

2b(sqrt(5)sqrt(b))^2

(a * b)^m=a^m* b^m

2b(sqrt(5))^2(sqrt(b))^2

( sqrt(a) )^2 = a

2b(5)b

Now that we have simplified the factors as much as possible, we can use the Commutative Property of Multiplication to simplify even further.

2b(5)b

CommutativePropMult

Commutative Property of Multiplication

2(5)b* b

Multiply

10b* b

ProdToPowTwoFac

a* a=a^2

10b^2

Subchapter links

Lesson Check p.623

Practice and Problem-Solving Exercises p.623-625

Standardized Test Prep p.625

Mixed Review p.625