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5-6 Radical ExpressionsObjectivesStudents will be able to:1) Simplify radical expressions2) Add, subtract, multiply, and divide radical expressions
What is a square root?• A square root is one of two equal factors of a number.
• Is that the only square root of 9?
Perfect Squares• A number that has an integer value as its square root is what is
known as a perfect square. For example, 4 is a perfect square because its square roots are 2 and -2 (both integers).• Can you name other perfect squares?
• Up to this point, we have only dealt with perfect squares as our radicands. How would we simplify a radical expression that does not have a perfect value as a radicand?
• Let’s examine the steps that could be applied to simplify square roots.
Steps to simplify a square root.1) Factor the radicand into as
many squares as possible.2) Isolate the perfect square
terms.3) Simplify each radical.
Addition/Subtraction of Square Roots• In order to add or subtract two square root expressions, the
terms must have the same radicand.• If the radicands are the same, you add/subtract the terms on
the outside of the radical expression, and keep the radicand.• You may need to simplify the terms before you can
add/subtract.
Multiplying Radical Expressions• When multiplying radical expressions, the terms on the
outside of the radicals get multiplied, and the radicands get multiplied. You then simplify, if possible.• If you choose, you can simplify the radical expressions first (if
possible), and then multiply.• When dividing radical expressions, divide the radicands, if
possible. Again, you may choose to simplify first (if possible).
• Who wants to see some examples…
Rationalize the Denominator
• There can never be a radical in the denominator of a fraction. • If a denominator contains a radical, the
expression must be rationalized. This occurs by multiplying the entire expression by a form of the number 1. The goal is to multiply by a quantity so that the radicand has an exact root.• Let’s see what this all means…