1-3 Square Roots Warm Up Lesson Presentation Lesson Quiz Holt Algebra 2

Warm Up Round to the nearest tenth. 1. 3.14 2. 1.97 1. 3.14 2. 1.97 Find each square root. 3. 4. Write each fraction in simplest form. 5. 6. Simplify. 7. 8. 3.1 2.0 +, -4 +,-25

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

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.

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

Example 2: Simplifying Square–Root Expressions Simplify each expression. C. Product Property of Square Roots D. Quotient Property of Square Roots

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.

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

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.

Example 3A: Rationalizing the Denominator Simplify by rationalizing the denominator. Multiply by a form of 1. = 2

Example 3B: Rationalizing the Denominator Simplify the expression. Multiply by a form of 1.

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

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

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.

Example 4A: Adding and Subtracting Square Roots

Example 4B: Adding and Subtracting Square Roots Simplify radical terms. Combine like radical terms.

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

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

6.7 Lesson Quiz: Part I 1. Estimate to the nearest tenth. Simplify each expression. 2. 3. 4. 5.

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