Chapter 8 Continued – Radical Expressions and Equations Multiplication & Division of Radical Expressions When multiplying radical expressions, you can just put everything that’s under a radical sign together under one big radical sign. Distributive Property: BE CAREFUL!

Example 3 Multiply Example Multiply Notice that when ra adical expression has two terms, all radicals disappear when you multiply the expression by its conjugate. Try this one:

Radical Expressions in Simplest Form A radical expression is in simplest form if: The radicand contains no factor greater than 1 that is a perfect square. There is no fraction under the radical sign. There is no radical in the denominator of a fraction. is not in simplest form because there is a fraction under the radical sign. This can be simplified by taking the square root of the numerator and the denominator.

Is not in simplest form because there is a radical expression in the denominator; The way to simplify is to multiply both numerator and denominator by This doesn’t always work when there is a two-term expression with at least one radical term added to another term. UGH! The trick for these types is to multiply the numerator and denominator by the conjugate. SIMPLIFIED!

Solving Equations Containing Radical Expressions Property of Squaring Both Sides of an Equation If a and b are real numbers and a=b, then a2=b2 It’s very important to check your solution because some “solutions” actually make the original equation untrue. Example: Notice that when you get the constants on one side, your equation says that the radical expression must equal a negative number. This is impossible! Therefore there is NO SOLUTION to an equation like this.

square both sides This is now a degree 2 equation so put it in standard form, factor it, then use zero-product rule. Impossible because the principal square root of a number can never be negative. Therefore -6 is not a possible solution. OK Therefore, only solution is {5}

You try! Solve: a = Solve equation and exclude any extraneous solutions: m =

Solve: