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McGraw Hill Glencoe Geometry, 2012

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McGraw Hill Glencoe Geometry, 2012 View details

1. Points, Lines, and Planes

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Exercise 73 Page 12

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

4sqrt(15)-8sqrt(3)

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 2-sqrt(5).

4sqrt(3)/2+sqrt(5)

a/b=a * (2-sqrt(5))/b * (2-sqrt(5))

4sqrt(3)(2-sqrt(5))/(2+sqrt(5))(2-sqrt(5))

Distribute 4sqrt(3)

4sqrt(3)* 2-4sqrt(3)*sqrt(5)/(2+sqrt(5))(2-sqrt(5))

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

4sqrt(3)* 2-4sqrt(3* 5)/(2+sqrt(5))(2-sqrt(5))

Multiply

8sqrt(3)-4sqrt(15)/(2+sqrt(5))(2-sqrt(5))

ExpandDiffSquares

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

8sqrt(3)-4sqrt(15)/2^2-(sqrt(5))^2

Calculate power

8sqrt(3)-4sqrt(15)/4-5

Subtract term

8sqrt(3)-4sqrt(15)/- 1

▼

Simplify

MoveNegDenomToNum

Put minus sign in numerator

- (8sqrt(3)-4sqrt(15))/1

a/1=a

- (8sqrt(3)-4sqrt(15))

Distribute - 1

- 8sqrt(3)+4sqrt(15)

CommutativePropAdd

Commutative Property of Addition

4sqrt(15)-8sqrt(3)

Subchapter links

Check Your Understanding p.8

Practice and Problem Solving p.8-11

H.O.T. Problems p.11

Standardized Test Practice p.12

Spiral Review p.12

Skills Review p.12