Lesson 103 Dividing radical expressions Quotient property of

Lesson 103 Dividing radical expressions

Quotient property of radicals

Rationalizing the denominator l l l A radical expression in simplest form cannot have a fraction for a radicand or a radical in the denominator. To rationalize a denominator means to use a method which removes radicals from the denominator of a fraction. A fraction is multiplied by another fraction equal to 1 in order to remove the radical from the denominator.

Rationalizing the denominator l Simplify

practice l Simplify:

Rationalizing a variable denominator l simplify

practice

Simplifying before rationalizing the denominator

practice

Conjugate of an irrational number l The conjugate of an irrational number in the form is l The conjugate is used to rationalize the denominator when it is a binomial with a radical

Using conjugates to rationalize the denominator

practice

Lesson 106 l. Solving radical equations

Radical equation An equation containing a variable in a radicand is called a radical equation. l Inverse operations are used to solve radical equations. l The inverse of finding the square root of a term is squaring a term. l

Solving simple radical equations

solve

Solving by isolating the square root

Solving with square roots on both sides

solve

Determining extraneous solutions l When both sides of an equation are squared to solve an equation, the resulting equation may have solutions that do not satisfy the original equation- these are extraneous solutions.

solve

solve