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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 47 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.

5sqrt(6)-5sqrt(3)/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 sqrt(6)-sqrt(3).

5/sqrt(6)+sqrt(3)

a/b=a * (sqrt(6)-sqrt(3))/b * (sqrt(6)-sqrt(3))

5(sqrt(6)-sqrt(3))/(sqrt(6)+sqrt(3))(sqrt(6)-sqrt(3))

▼

Distribute 5

Distribute 5

5* sqrt(6)-5* sqrt(3)/(sqrt(6)+sqrt(3))(sqrt(6)-sqrt(3))

Multiply

5sqrt(6)-5sqrt(3)/(sqrt(6)+sqrt(3))(sqrt(6)-sqrt(3))

ExpandDiffSquares

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

5sqrt(6)-5sqrt(3)/(sqrt(6))^2-(sqrt(3))^2

( sqrt(a) )^2 = a

5sqrt(6)-5sqrt(3)/6-3

Subtract term

5sqrt(6)-5sqrt(3)/3

Subchapter links

Exercises p.248-250