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Published byBernard McCarthy Modified over 7 years ago

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In order to add or subtract radicals: All radicals must be simplified. Then, you combine “like” terms. Square-root expressions with the same radicand are examples of like radicals.

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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.

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Example 1 Add or subtract. A. The terms are like radicals. B. The terms are unlike radicals. Do not combine.

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Sometimes radicals do not appear to be like until they are simplified, Simplify all radicals in an expression before trying to identify like radicals.

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Example 2 Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. Combine like radicals.

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Example 3 Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. The terms are unlike radicals. Do not combine.

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Example 4 Simplify each expression. Factor the radicands using perfect squares. Product Property of Square Roots. Simplify. The terms are unlike radicals. Do not combine.

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Example 5 Find the perimeter of the triangle. Give the answer as a radical expression in simplest form. Write an expression for perimeter. Factor 20 using a perfect square. Product Property of Square Roots. Simplify. Combine like radicals.

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Try these… Add or subtract. 1. 2. Simplify each expression. 3. 4. 5.

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6. Find the perimeter of the trapezoid. Give the answer as a radical expression is simplest form.

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