Lesson 11 3 Adding and Subtracting Radical Expressions

Lesson 11. 3 Adding and Subtracting Radical Expressions

California Standards Extension of 2. 0 Students understand use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand 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 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.

Helpful Hint Combining like radicals is similar to combining like terms.

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. the terms are like radicals. Combine like radicals. D. Identify like radicals. Combine like radicals.

Now You Try Add or subtract. 1. The terms are like radicals. Combine like radicals. 2. Identify 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.

Remember! When you write a radicand as a product, make at least one factor a perfect square.

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 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.

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.

Lesson Quiz Add or subtract. 1. 2. 3. Simplify each expression. 4. 5.