Post on 24-Dec-2015
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