Binomial Radical Expressions

Like Radicals Have the same index

and the same radicand.

Examples

x x

3 3xy xy

4 3x y Can’t be done!

Adding and Subtracting Radical Expressions To add and subtract like radicals, use the

Distributive Property.

Examples3(5 3) x 3 35 3x x 38 x

4 2 5 3 Can’t be added, not like radicands

2 7 3 7 (2 3) 7 5 7

3 37 5 2 5 3(7 2) 5 35 5

Simplifying Before Adding or Subtracting

6 18 4 8 6 9 2 4 4 2 6 3 2 4 2 2

18 2 8 2

26 2

*Simplify the radical, then add or subtract

Multiplying Binomial Radical Expressions

Use FOIL to multiply First Outer Inner Last

Conjugates Expressions such as and that

differ in only the sign of the second term.a b a b

Multiplying Conjugates

2 2a b a b a b

Rationalizing Binomial Radical Denominators Sometimes you need to rationalize the

denominator of a fraction when the denominator is a binomial radical expression

Multiply the numerator and denominator of the fraction by the conjugate of the denominator

numerator conjugate of denominator

denominator conjugate of denominator