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Pearson Algebra 1 Common Core, 2011 – Simplifying Radicals

30a^4

Solution

We want to simplify a radical expression. To do so we will assume that a≥0, otherwise the given expression would not be defined. sqrt(45a^7)* sqrt(20a) 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(45a^7)* sqrt(20a)

SplitIntoFactors

Split into factors

sqrt(9* 5* a^2* a^2* a^2* a)* sqrt(4* 5* a)

SqrtProd

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

sqrt(9)sqrt(5)sqrt(a^2)sqrt(a^2)sqrt(a^2)sqrt(a)* sqrt(4)sqrt(5)sqrt(a)

▼

Simplify

CalcRoot

Calculate root

3sqrt(5)sqrt(a^2)sqrt(a^2)sqrt(a^2)sqrt(a)* 2sqrt(5)sqrt(a)