Post on 08-Feb-2016
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Lesson 11.3
Adding and Subtracting Radical Expressions
California Standards
Extension of 2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
Square-root expressions with the same radicand are examples of like radicals.
Like radicals can be combined by adding or subtracting. You can use the Distributive Property to show how this is done:
Notice that you can combine like radicals by adding or subtracting the numbers multiplied by the radical and keeping the radical the same.
Combining like radicals is similar to combining like terms.Helpful Hint
Adding and Subtracting Square-Root Expressions
Add or subtract.
A.
The terms are like radicals.
B.
The terms are unlike radicals. Do not combine.
Adding and Subtracting Square-Root Expressions
Add or subtract.
C.
D.
Identify like radicals.
Combine like radicals.
the terms are
like radicals.Combine like radicals.
Now You Try
Add or subtract.
1.
The terms are like radicals.
2.
Identify like radicals.
Combine like radicals.
Combine like radicals.
Sometimes radicals do not appear to be like until they are simplified. Simplify all radicals in an expression before trying to identify like radicals.
Simplify Before Adding or Subtracting
Simplify each expression. All variables represent nonnegative numbers.
Factor the radicands using perfect squares.
Product Property of Square Roots
Simplify.
Combine like radicals.
Simplify Before Adding or Subtracting
Simplify each expression. All variables represent nonnegative numbers.
Factor the radicands using perfect squares.
Product Property of Square Roots
Simplify.
The terms are unlike radicals. Do not combine.
When you write a radicand as a product, make at least one factor a perfect square.
Remember!
Let’s Try One More…
Simplify each expression. All variables represent nonnegative numbers.
Factor the radicands using perfect squares.
Product Property of Square Roots
Simplify.
Combine like radicals.
Now You Try
Factor the radicands using perfect squares.
Product Property of Square Roots
Simplify.
The terms are unlike radicals. Do not combine.
Simplify each expression. All variables represent nonnegative numbers.
One More…
Factor the radicands using perfect squares.
Product Property of Square Roots
Simplify.
Combine like radicals.
Simplify each expression. All variables represent nonnegative numbers.
Lesson Quiz
Add or subtract.
1.
2.
Simplify each expression.
3.
4.
5.