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**1-3 Square Roots Warm Up Lesson Presentation Lesson Quiz**

Holt Algebra 2

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**Warm Up Round to the nearest tenth. 1. 3.14 2. 1.97**

Find each square root. Write each fraction in simplest form. Simplify. 3.1 2.0 +, -4 +,-25

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**Square roots have special properties that help you simplify, multiply, and divide them.**

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Notice that these properties can be used to combine quantities under the radical symbol or separate them for the purpose of simplifying square-root expressions. A square-root expression is in simplest form when the radicand has no perfect-square factors (except 1) and there are no radicals in the denominator.

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**Example 2: Simplifying Square–Root Expressions**

Simplify each expression. A. Find a perfect square factor of 32. Product Property of Square Roots B. Quotient Property of Square Roots

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**Example 2: Simplifying Square–Root Expressions**

Simplify each expression. C. Product Property of Square Roots D. Quotient Property of Square Roots

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**Simplify each expression.**

Check It Out! Example 2 Simplify each expression. A. Find a perfect square factor of 48. Product Property of Square Roots B. Quotient Property of Square Roots Simplify.

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**Simplify each expression.**

Check It Out! Example 2 Simplify each expression. C. Product Property of Square Roots D. Quotient Property of Square Roots

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If a fraction has a denominator that is a square root, you can simplify it by rationalizing the denominator. To do this, multiply both the numerator and denominator by a number that produces a perfect square under the radical sign in the denominator.

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**Example 3A: Rationalizing the Denominator**

Simplify by rationalizing the denominator. Multiply by a form of 1. = 2

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**Example 3B: Rationalizing the Denominator**

Simplify the expression. Multiply by a form of 1.

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Check It Out! Example 3a Simplify by rationalizing the denominator. Multiply by a form of 1.

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Check It Out! Example 3b Simplify by rationalizing the denominator. Multiply by a form of 1.

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**Square roots that have the same radicand are called like radical terms.**

To add or subtract square roots, first simplify each radical term and then combine like radical terms by adding or subtracting their coefficients.

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**Example 4A: Adding and Subtracting Square Roots**

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**Example 4B: Adding and Subtracting Square Roots**

Simplify radical terms. Combine like radical terms.

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Check It Out! Example 4a Add or subtract. Combine like radical terms.

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Check It Out! Example 4b Add or subtract. Simplify radical terms. Combine like radical terms.

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**6.7 Lesson Quiz: Part I 1. Estimate to the nearest tenth.**

Simplify each expression. 2. 3. 4. 5.

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Lesson Quiz: Part II Simplify by rationalizing each denominator. 6. 7. Add or subtract. 8. 9.

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