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Rationalizing the Denominator. Binomial Denominators. Presented by Kathryn Maloney. Rationalizing the Denominator. (1) Multiply both the numerator and denominator by the conjugate of the denominator . (2) Simplify the result. Cool Math Term. Conjugate Surd. - PowerPoint PPT Presentation
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Rationalizing the Denominator
Presented byKathryn Maloney
Binomial Denominators
Rationalizing the Denominator
(1) Multiply both the numerator and denominator by the conjugate of the denominator.(2) Simplify the result.
Cool Math Term
(√𝒃)Conjugate SurdA surd is a root that can’t be simplified further.
Product of Two Conjugates(𝒂+√𝒃) (𝒂−√𝒃 )
𝒂𝟐− (√𝒃 )𝟐
𝒂𝟐−𝒃
Product of the sum and difference of two terms.
𝒂𝟐−𝒂 √𝒃+𝒂√𝒃− (√𝒃 )𝟐FOIL!
63+√5
Perform the indicate division. (Rationalize the denominator)
What is the conjugate of the denominator?
𝟑−√𝟓6
3+√5𝟑−√𝟓𝟑−√𝟓¿
6 (3−√5 )32−5
¿6 (3−√5 )
4¿3 (3−√5 )
2
12+√3
Perform the indicate division. (Rationalize the denominator)
You Try!
Press pause, find the solution, and play to check your answer!
12+√3
Perform the indicate division. (Rationalize the denominator)
What is the conjugate of the denominator?
𝟐−√𝟑1
2+√3𝟐−√𝟑𝟐−√𝟑¿
1 (2−√3 )22−3
¿(2−√3 )1
¿2−√3
You
Try!
3−√24+√2
Perform the indicate division. (Rationalize the denominator)
What is the conjugate of the denominator?4
3−√24+√2
𝟒−√𝟐𝟒−√𝟐
¿(3−√2 ) (4−√2 )
42−2
¿ 12−3√2−4 √2+214 ¿ 14−7 √2
14
¿7 (2−√2 )14
¿ 2−√22
FOIL
2+√31−√3
Perform the indicate division. (Rationalize the denominator)
You Try!
Press pause, find the solution, and play to check your answer!
2+√31−√3
Perform the indicate division. (Rationalize the denominator)
What is the conjugate of the denominator?
1
2+√31−√3
𝟏+√𝟑𝟏+√𝟑
¿(2+√3 ) (1+√3 )
12−3
¿ 2+2√3+√3+3−2 ¿− 5+3√32
You
Try!
FOIL
3√2+12√2−1
Perform the indicate division. (Rationalize the denominator)
What is the conjugate of the denominator?
2√2+1
¿(3√2+1 ) (2√2+1 )
(2√2 )2−12
¿6(2)+3√2+2√2+1
8−1 ¿ 13+5√27
3√2+12√2−1
2√2+12√2+1
FOIL
2√2+33√2+2
Perform the indicate division. (Rationalize the denominator)
You Try!
Press pause, find the solution, and play to check your answer!
2√2+33√2+2
Perform the indicate division. (Rationalize the denominator)
What is the conjugate of the denominator?
3√2−2
¿(2√2+3 ) (3√2−2 )
(3√2 )2−22
¿6 (2 )−4√2+9√2−6
18−4 ¿ 6+5 √214
You
Try!
2√2+33√2+2
3√2−23√2−2
FOIL
Thank you!
Don't worry about moving slowly, worry about standing still. -- Chinese proverb
