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Pearson Algebra 1 Common Core, 2011 View details

2. Simplifying Radicals

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Exercise 40 Page 623

Use the Multiplication Property of Square Roots and the Division Property of Square Roots.

-45t

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that t>0, otherwise the given expression would not be defined. - 5sqrt(162t^3/2t)Let's recall the Multiplication Property of Square Roots and the Division Property of Square Roots. sqrt(ab)=sqrt(a) * sqrt(b), for a≥ 0,b≥ 0 sqrt(a/b)=sqrt(a)/sqrt(b), for a≥ 0,b> 0 Let's use these properties for our expression.

-5sqrt(162t^3/2t)

SqrtQuot

sqrt(a/b)=sqrt(a)/sqrt(b)

-5sqrt(162t^3)/sqrt(2t)

SplitIntoFactors

Split into factors

-5sqrt(81* 2* t^2* t)/sqrt(2* t)

SqrtProd

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

-5sqrt(81)* sqrt(2)* sqrt(t^2)* sqrt(t)/sqrt(2)* sqrt(t)

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Simplify Factors