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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Simplifying Radical Expressions

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Exercise 14 Page 248

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

2-sqrt(3)/2

Practice makes perfect

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 4-sqrt(12).

1/4+sqrt(12)

a/b=a * (4-sqrt(12))/b * (4-sqrt(12))

1(4-sqrt(12))/(4+sqrt(12))(4-sqrt(12))

Identity Property of Multiplication

4-sqrt(12)/(4+sqrt(12))(4-sqrt(12))

ExpandDiffSquares

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

4-sqrt(12)/4^2-(sqrt(12))^2

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Calculate power

Calculate power

4-sqrt(12)/16-(sqrt(12))^2

( sqrt(a) )^2 = a

4-sqrt(12)/16-12

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Simplify Factors

SplitIntoFactors

Split into factors

4-sqrt(4* 3)/16-12

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

4-sqrt(4)sqrt(3)/16-12

Calculate root

4-2sqrt(3)/16-12

Subtract term

4-2sqrt(3)/4

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

4-2sqrt(3)/4

Factor out 2

2(2-sqrt(3))/2(2)

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

2-sqrt(3)/2

Subchapter links

Exercises p.248-250