1 3 Square Roots Warm Up Lesson Presentation

1 -3 Square Roots Warm Up Lesson Presentation Lesson Quiz Holt Algebra 22

1 -3 Square Roots Warm Up Round to the nearest tenth. 1. 3. 14 3. 1 2. 1. 97 2. 0 Find each square root. 3. +, -4 4. +, -25 Write each fraction in simplest form. 5. 6. Simplify. 7. Holt Algebra 2 8.

1 -3 Square Roots Square roots have special properties that help you simplify, multiply, and divide them. Holt Algebra 2

1 -3 Square Roots Holt Algebra 2

1 -3 Square Roots 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. Holt Algebra 2

1 -3 Square Roots 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 Holt Algebra 2

1 -3 Square Roots Example 2: Simplifying Square–Root Expressions Simplify each expression. C. Product Property of Square Roots D. Quotient Property of Square Roots Holt Algebra 2

1 -3 Square Roots 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. Holt Algebra 2

1 -3 Square Roots Check It Out! Example 2 Simplify each expression. C. Product Property of Square Roots D. Quotient Property of Square Roots Holt Algebra 2

1 -3 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. Holt Algebra 2

1 -3 Square Roots Example 3 A: Rationalizing the Denominator Simplify by rationalizing the denominator. Multiply by a form of 1. =2 Holt Algebra 2

1 -3 Square Roots Example 3 B: Rationalizing the Denominator Simplify the expression. Multiply by a form of 1. Holt Algebra 2

1 -3 Square Roots Check It Out! Example 3 a Simplify by rationalizing the denominator. Multiply by a form of 1. Holt Algebra 2

1 -3 Square Roots Check It Out! Example 3 b Simplify by rationalizing the denominator. Multiply by a form of 1. Holt Algebra 2

1 -3 Square Roots 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. Holt Algebra 2

1 -3 Square Roots Example 4 A: Adding and Subtracting Square Roots Add. Holt Algebra 2

1 -3 Square Roots Example 4 B: Adding and Subtracting Square Roots Subtract. Simplify radical terms. Combine like radical terms. Holt Algebra 2

1 -3 Square Roots Check It Out! Example 4 a Add or subtract. Combine like radical terms. Holt Algebra 2

1 -3 Square Roots Check It Out! Example 4 b Add or subtract. Simplify radical terms. Combine like radical terms. Holt Algebra 2

1 -3 Square Roots Lesson Quiz: Part I 1. Estimate to the nearest tenth. Simplify each expression. 2. 3. 4. 5. Holt Algebra 2 6. 7

1 -3 Square Roots Lesson Quiz: Part II Simplify by rationalizing each denominator. 6. 7. Add or subtract. 8. 9. Holt Algebra 2