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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 76 Page 625

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

30a^4

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that a≥0, otherwise the given expression would not be defined. sqrt(45a^7)* sqrt(20a) 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(45a^7)* sqrt(20a)

SplitIntoFactors

Split into factors

sqrt(9* 5* a^2* a^2* a^2* a)* sqrt(4* 5* a)

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

sqrt(9)sqrt(5)sqrt(a^2)sqrt(a^2)sqrt(a^2)sqrt(a)* sqrt(4)sqrt(5)sqrt(a)

▼

Simplify

Calculate root

3sqrt(5)sqrt(a^2)sqrt(a^2)sqrt(a^2)sqrt(a)* 2sqrt(5)sqrt(a)

SqrtPowToNumber

sqrt(a^2)=a

3sqrt(5)a* a* asqrt(a)* 2sqrt(5)sqrt(a)

ProdToPowThreeFac

a* a* a=a^3

3sqrt(5)a^3sqrt(a)* 2sqrt(5)sqrt(a)

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

3sqrt(5)a^3sqrt(a)* 2sqrt(5)sqrt(a)

CommutativePropMult

Commutative Property of Multiplication

3(2)a^3sqrt(5)sqrt(5)sqrt(a)sqrt(a)

Multiply

6a^3sqrt(5)sqrt(5)sqrt(a)sqrt(a)

sqrt(a)* sqrt(a)= a

6a^35a

▼

Simplify

CommutativePropMult

Commutative Property of Multiplication

6(5)a^3* a

Multiply

30a^3* a

a^m*a^n=a^(m+n)

30a^4

Subchapter links

Lesson Check p.623

Practice and Problem-Solving Exercises p.623-625

Standardized Test Prep p.625

Mixed Review p.625