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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 33 Page 623

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

24c^7

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that c≥ 0, otherwise the given expression would not be defined. - 1/3sqrt(18c^5) * (- 6sqrt(8c^9)) 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.

- 1/3sqrt(18c^5) * (- 6sqrt(8c^9))
SplitIntoFactors

Split into factors

- 1/3sqrt(9* 2* c^2* c^2* c) * (- 6sqrt(4* 2* c^2* c^2* c^2* c^2* c))
SqrtProd

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

- 1/3sqrt(9)sqrt(2)sqrt(c^2)sqrt(c^2)sqrt(c) * (- 6sqrt(4)sqrt(2)sqrt(c^2)sqrt(c^2)sqrt(c^2)sqrt(c^2)sqrt(c))
â–¼
Simplify factors
CalcRoot

Calculate root

- 1/3(3)sqrt(2)sqrt(c^2)sqrt(c^2)sqrt(c) * (- 6(2)sqrt(2)sqrt(c^2)sqrt(c^2)sqrt(c^2)sqrt(c^2)sqrt(c))
SqrtPowToNumber

sqrt(a^2)=a

- 1/3(3)sqrt(2)c* csqrt(c) * (- 6(2)sqrt(2)c* c* c* csqrt(c))
MultPow

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

- 1/3(3)sqrt(2)c^2sqrt(c) * (- 6(2)sqrt(2)c^4sqrt(c))
FracMultDenomToNumber

a/3* 3 = a

- 1sqrt(2)c^2sqrt(c) * (- 6(2)sqrt(2)c^4sqrt(c))
MultNegPos

(- a)b = - ab

- 1sqrt(2)c^2sqrt(c) * (- 12sqrt(2)c^4sqrt(c))

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

- 1sqrt(2)c^2sqrt(c) * (- 12sqrt(2)c^4sqrt(c))
CommutativePropMult

Commutative Property of Multiplication

-1(-12)c^4c^2sqrt(2)sqrt(2)sqrt(c)sqrt(c)
MultNegNegOnePar

- a(- b)=a* b

12c^4c^2sqrt(2)sqrt(2)sqrt(c)sqrt(c)
MultSqrt

sqrt(a)* sqrt(a)= a

12c^4c^22c
â–¼
Simplify Factors
CommutativePropMult

Commutative Property of Multiplication

12(2)c^4c^2c
Multiply

Multiply

24c^4c^2c
MultPow

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

24c^7
Subchapter links expand_more
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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