Exercise 44 Page 249

To rationalize a fraction with a binomial denominator, we multiply the numerator and denominator of the fraction by the conjugate of the denominator. We find the conjugate by changing the sign of the second term of the expression.

Binomial	Conjugate
a + b	a - b
a - b	a + b

In this case, the conjugate of the denominator is 6+sqrt(8).

9/6-sqrt(8)

ExpandFrac

a/b=a * (6+sqrt(8))/b * (6+sqrt(8))

9(6+sqrt(8))/(6-sqrt(8))(6+sqrt(8))

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Distribute 9

Distr

Distribute 9

9* 6+9* sqrt(8)/(6-sqrt(8))(6+sqrt(8))

Multiply

Multiply

54+9sqrt(8)/(6-sqrt(8))(6+sqrt(8))

(a-b)(a+b)=a^2-b^2

54+9sqrt(8)/6^2-(sqrt(8))^2

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Calculate power

CalcPow

Calculate power

54+9sqrt(8)/36-(sqrt(8))^2

PowSqrt

( sqrt(a) )^2 = a

54+9sqrt(8)/36-8

SubTerm

Subtract term

54+9sqrt(8)/28

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Simplify Factors

SplitIntoFactors

Split into factors

54+9sqrt(4* 2)/28

SqrtProd

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

54+9sqrt(4)sqrt(2)/28

CalcPow

Calculate power

54+9(2)sqrt(2)/28

FactorOut

Factor out 2

2(27+9sqrt(2))/2(14)

ReduceFrac

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

27+9sqrt(2)/14