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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 67 Page 624

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

ab^2csqrt(abc)

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that a≥0, b≥0 and c≥0 otherwise the given expression would not be defined. sqrt(a^3b^5c^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.

sqrt(a^3b^5c^3)
SplitIntoFactors

Split into factors

sqrt(a^2* a* b^2* b^2* b* c^2* c)
SqrtProd

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

sqrt(a^2)sqrt(a)sqrt(b^2)sqrt(b^2)sqrt(b)sqrt(c^2)sqrt(c)
SqrtPowToNumber

sqrt(a^2)=a

asqrt(a)b* bsqrt(b)csqrt(c)
ProdToPowTwoFac

a* a=a^2

asqrt(a)b^2sqrt(b)csqrt(c)
CommutativePropMult

Commutative Property of Multiplication

ab^2csqrt(a)sqrt(b)sqrt(c)
ProdSqrt

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

ab^2csqrt(abc)
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arrow_right Lesson Check p.623
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Lesson Check 9 (Page 623)
arrow_right Practice and Problem-Solving Exercises p.623-625
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arrow_right Standardized Test Prep p.625
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arrow_right Mixed Review p.625
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