Exercise 74 Page 625

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

12x

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that x≥0, otherwise the given expression would not be defined. sqrt(24)* sqrt(2x)* sqrt(3x) 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(24)* sqrt(2x)* sqrt(3x)

SplitIntoFactors

Split into factors

sqrt(4* 2* 3)* sqrt(2* x)* sqrt(3* x)

SqrtProd

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

sqrt(4)sqrt(2)sqrt(3)* sqrt(2)sqrt(x)* sqrt(3)sqrt(x)

CalcRoot

Calculate root

2sqrt(2)sqrt(3)* sqrt(2)sqrt(x)* sqrt(3)sqrt(x)

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

2sqrt(2)sqrt(3)* sqrt(2)sqrt(x)* sqrt(3)sqrt(x)