Multiplying and Dividing Radical Expressions Binomial Radical Expressions

Multiplying and Dividing Radical Expressions. Binomial Radical Expressions. n r a e l ’ll u o y What To multiply and divide radical expressions. To add and subtract radical expressions. a c o V ry a l bu Simplest form of a radical, rationalize the denominator, like radicals

Take a note: You can simplify the product of powers that have the same exponent. Similarly, you can simplify the product of radicals that have the same index You can simplify a radical expression when the exponen of one factor of the radicand is a multiple of the radical’s index. Example:

Problem 1: Multiplying Radical Expressions. Can you simplify the product of the radical expressions? Explain. Your turn Can you simplify the product of the radical expressions? Explain. Answer:

If the radicand has a perfect nth power among its factors, you can reduce the radical. . If you reduce a radical as much as possible, the radical is in the simplest form Problem 2: Simplifying a radical Expression Your turn Answer:

Problem 3: Simplifiying a Product Answer Your turn Answers:

You can extend the property for multiplying radical expressions. If the indexes are the same , you can write a quotient of roots as a root of quotient. Problem 4: Dividing Radical Expressions What is the simplest form of the quotient?

Your turn Answer: Note: Another way to simplify an expression is to rationalize the denominator. You rewrite the expression so that there are no radicals in any denominator and no denominator in any radical. Do the factorization of the denominator and choose what to multiply by. What do you need to make each factor of the radicand in the denominator a perfect cube. Problem 5: Rationalizing the Denominator What the denominator is missing to get out of the radical?

Your turn Answer: Take a note: Like radicals are radical expressions that have the same index and radicand. You can combine like radicals using properties of real numbers. When adding or subtracting remember to simplify first. When multiplying binomial radicals expressions use FOIL

Problem 6: Adding and Subtracting Radical Expressions What is the simplified form of each expression? The radicands are different. You cannot combine the expressions The indexes are different. You cannot combine the expressions Your turn What is the simplified form of each expression? The indexes are different. You cannot combine the expressions

Your turn again: Using radical expression 1. )This tile design is made of congruent right triangles with base 1 ft and height 2 ft. Find the perimeter of the tile to the nearest tenth of a foot. Answer: Hint use P. T. to find c 2. ) What is the simplest form of the expression? (remember to simplified before adding or subtracting) Answer:

Problem 7: Multiplying Binomial Radical Expressions What is the product of each radical expression? Multiplying conjugates Your turn: What is the product of each radical expression Answers:

Problem 8: Rationalizing the denominator How can you write the expression with a rationalized denominator? Take a note: Conjugate are expressions that only differ in the signs of the second term Your turn: How can you write the expression with a rationalized denominator Answer

Classwork odd Homework even TB pgs 371 -372 exercises 10 -68 TB pgs 378 -378 exercises 10 -64