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Pearson Algebra 1 Common Core, 2011

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Pearson Algebra 1 Common Core, 2011 View details

Chapter Review

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Exercise 28 Page 654

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

30t^4sqrt(3)

Practice makes perfect

We want to simplify a radical expression. 6 sqrt(5t^3) * sqrt(15 t^5) 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.

6 sqrt(5t^3) * sqrt(15 t^5)

SplitIntoFactors

Split into factors

6 sqrt(5* t* t^2) * sqrt(5* 3* t* t^2 * t^2)

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

6 sqrt(5) * sqrt(t) * sqrt(t^2) * sqrt(5) * sqrt(3) * sqrt(t) * sqrt(t^2) * sqrt(t^2)

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

6 sqrt(5) * sqrt(t) * sqrt(t^2) * sqrt(5) * sqrt(3) * sqrt(t) * sqrt(t^2) * sqrt(t^2)

CommutativePropMult

Commutative Property of Multiplication

6sqrt(5) * sqrt(5) * sqrt(t) * sqrt(t) * sqrt(t^2) * sqrt(t^2) * sqrt(t^2) * sqrt(3)

sqrt(a)* sqrt(a)= a

6* 5* t*sqrt(t^2)*sqrt(t^2)*sqrt(t^2)*sqrt(3)

SqrtPowToNumber

sqrt(a^2)=a

6 * 5 * t* t* t* t* sqrt(3)

a* ... * a_(n times) = a^n

6* 5 t^4 sqrt(3)

Multiply

30t^4 sqrt(3)

Subchapter links

Exercises p.653-656