Multiplying Binomial Radial Expressions and Rationalizing with Conjugates. MA.912.A.6.2 Add, subtract, multiply, and divide radical expressions (Square roots and higher)

Multiplying Radical Expressions Distributive Property Product Property Of Radicals Ask students what they could have done differently to still come up with the same answer– they could have simplified radical 20 to 2 radical 5 before using the distributive property. Simplify

Multiplying Radical Expressions Ask students what they could have done differently to still come up with the same answer– they could have simplified radical 20 to 2 radical 5 before using the distributive property.

Multiplying Radical Expressions Since there are no like terms, you can not combine.

Conjugate Binomials The conjugate of When you multiply conjugate binomials, The product will be: The Difference of Squares.

Conjugate Binomials The conjugate of

Multiplying Conjugates What other method would yield the same answer with less work?

Multiplying Conjugates

Rationalizing Using Conjugates You should recall that a radical expression is not considered simplified if there is a radical in the denominator. The process of eliminating the radical in the denominator is called rationalizing.

Rationalizing Using Conjugates When the denominator contains a binomial with a radical, one must multiply by the conjugate in order to rationalize the denominator. Multiplying by 1 does not change the value of the number. NO RADICAL!

Rationalizing Using Conjugates Simplify: Multiply by the conjugate. Multiply numerators Multiply denominators. Combine like terms Finished on next slide.

Combine like terms Never leave Negative in the Denominator! Distribute