Exercise 6 Page 461

To rationalize a monomial denominator, we multiply the numerator and denominator by a radical that will eliminate the radical in the denominator. Because the denominator is a square root, we need to multiply it by a square root that will give us a perfect square under the radical.

12/sqrt(6)

ExpandFrac

a/b=a * sqrt(6)/b * sqrt(6)

12sqrt(6)/sqrt(6)* sqrt(6)

ProdSqrt

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

12sqrt(6)/sqrt(6*6)

ProdToPowTwoFac

a* a=a^2

12sqrt(6)/sqrt(6^2)

SqrtPowToNumber

sqrt(a^2)=a

12sqrt(6)/6

We know that we have successfully rationalized the denominator because the radical has been eliminated. However, our fraction can still simplified a bit further. Let's try!

12sqrt(6)/6

ReduceFrac

a/b=.a /6./.b /6.

2sqrt(6)/1

DivByOne

a/1=a

2sqrt(6)