Exercise 46 Page 623

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

sqrt(2)/t^2

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. 2sqrt(24/48t^4) 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.

2sqrt(24/48t^4)

SqrtQuot

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

2sqrt(24)/sqrt(48t^4)

SplitIntoFactors

Split into factors

2sqrt(24)/sqrt(24* 2* t^2* t^2)

SqrtProd

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

2sqrt(24)/sqrt(24)* sqrt(2)* sqrt(t^2)* sqrt(t^2)

SqrtPowToNumber

sqrt(a^2)=a

2sqrt(24)/sqrt(24)* sqrt(2)t* t

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Simplify Factors

ProdToPowTwoFac

a* a=a^2

2sqrt(24)/sqrt(24)* sqrt(2)t^2

ReduceFrac

a/b=.a /sqrt(24)./.b /sqrt(24).

21/sqrt(2)t^2

MoveLeftFacToNumOne

a* 1/b= a/b

2/sqrt(2)t^2

Now that we have simplified the factors as much as possible, we need to rationalize the denominator. To do this, we will multiply the numerator and denominator by a square root that will eliminate the radical in the denominator.

2/sqrt(2)t^2

ExpandFrac

a/b=a * sqrt(2)/b * sqrt(2)

2* sqrt(2)/sqrt(2)t^2* sqrt(2)

CommutativePropMult

Commutative Property of Multiplication

2* sqrt(2)/sqrt(2)sqrt(2)* t^2

MultSqrt

sqrt(a)* sqrt(a)= a

2* sqrt(2)/2* t^2

ReduceFrac

a/b=.a /2./.b /2.