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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 19 Page 267

To rationalize a fraction with a binomial denominator, we multiply the numerator and denominator of the fraction by the conjugate of the denominator.

-3-3 sqrt(2)

To simplify the given radical expression we need to rationalize a fraction with a binomial denominator. To do this, we multiply the numerator and denominator of the fraction by the conjugate of the denominator. First, we will 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 1+sqrt(2).

3/1-sqrt(2)

a/b=a * (1+sqrt(2))/b * (1+sqrt(2))

3(1+sqrt(2))/(1-sqrt(2))(1+sqrt(2))

Distribute 3

3+3 sqrt(2)/(1-sqrt(2))(1+sqrt(2))

ExpandDiffSquares

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

3+3 sqrt(2)/1^2-(sqrt(2))^2

1^a=1

3+3 sqrt(2)/1-(sqrt(2))^2

( sqrt(a) )^2 = a

3+3 sqrt(2)/1-2

Subtract term

3+3 sqrt(2)/-1

MoveNegDenomToNum

Put minus sign in numerator

-(3+3 sqrt(2))/1

a/1=a

-(3+3 sqrt(2))

Distribute -1

-3-3 sqrt(2)