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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 32 Page 623

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

120x^3sqrt(2)

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that x≥ 0, otherwise the given expression would not be defined. 10sqrt(12x^3) * 2sqrt(6x^3) 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.

10sqrt(12x^3) * 2sqrt(6x^3)

SplitIntoFactors

Split into factors

10sqrt(6* 2* x^2* x) * 2sqrt(6* x^2* x)

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

10sqrt(6)sqrt(2)sqrt(x^2)sqrt(x) * 2sqrt(6)sqrt(x^2)sqrt(x)

( sqrt(a) )^2 = a

10sqrt(6)sqrt(2)xsqrt(x) * 2sqrt(6) xsqrt(x)

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

10sqrt(6)sqrt(2)xsqrt(x) * 2sqrt(6) xsqrt(x)

CommutativePropMult

Commutative Property of Multiplication

10(2)x* x* sqrt(6)sqrt(6)sqrt(2)sqrt(x)sqrt(x)

sqrt(a)* sqrt(a)= a

10(2)x* x* 6sqrt(2)x

Multiply

20x* x* 6sqrt(2)x

▼

Simplify Factors

CommutativePropMult

Commutative Property of Multiplication

20(6)x* x* xsqrt(2)

Multiply

120x* x* xsqrt(2)

ProdToPowThreeFac

a* a* a=a^3

120x^3sqrt(2)

Subchapter links

Lesson Check p.623

Practice and Problem-Solving Exercises p.623-625

Standardized Test Prep p.625

Mixed Review p.625