Prentice Hall Lesson 11. 1 How do you simplify a radical expression Prentice Hall Lesson 11.1 How do you simplify a radical expression? What is the multiplication property of square roots? BOP:

Solution to BOP: Possible Answer: The function is linear with a slope of -2 and y-intercept of 7.

Prentice Hall Lesson 11. 1 How do you simplify a radical expression Prentice Hall Lesson 11.1 How do you simplify a radical expression? What is the multiplication property of square roots? Toolbox: Radical expressions contain a radical Multiplication Property of Square Roots: For every number a ≥ 0 and b ≥ 0, √a•b = √a • √b To simplify radical expressions, rewrite the radicand as a product of perfect-square factors and the remaining factors. Simplify by taking the square root of the perfect-square factors, leaving the remaining factors as the radicand.

You may use the product of radicals to find perfect-square factors needed to simplify radical expressions. Division Property of Square Roots: For every number a ≥ 0 and b > 0, √ = √a √b When the denominator of the radicand is a perfect square, it is easier to simplify the numerator and denominator separately. When the denominator of the radicand is not a perfect square, divide first, then simplify.

When the radicand in the denominator is not a perfect square, you may need to rationalize the denominator. Multiply the numerator and denominator by the same radical expression, making the denominator a perfect square. A radical expression is in simplest radical form when all three statements are true: The radicand has no perfect-square factors other than 1. The radicand has no fractions. The denominator of a fraction has no radical.

= 81 • 3 Use the Multiplication Property of Square Roots. ALGEBRA 1 LESSON 11-1 Simplify 243. 243 = 81 • 3 81 is a perfect square and a factor of 243. = 81 • 3 Use the Multiplication Property of Square Roots. = 9 3 Simplify 81. 11-1

= 4x6 • 7x Use the Multiplication Property of Square Roots. ALGEBRA 1 LESSON 11-1 Simplify 28x7. 28x7 = 4x6 • 7x 4x6 is a perfect square and a factor of 28x7. = 4x6 • 7x Use the Multiplication Property of Square Roots. = 2x3 7x Simplify 4x6. 11-1

Simplify each radical expression. ALGEBRA 1 LESSON 11-1 Simplify each radical expression. a. 12 • 32 12 • 32 = 12 • 32 Use the Multiplication Property of Square Roots. = 384 Simplify under the radical. = 64 • 6 64 is a perfect square and a factor of 384. = 64 • 6 Use the Multiplication Property of Square Roots. = 8 6 Simplify 64. 11-1

7 5x • 3 8x = 21 40x2 Multiply the whole numbers and ALGEBRA 1 LESSON 11-1 (continued) b. 7 5x • 3 8x 7 5x • 3 8x = 21 40x2 Multiply the whole numbers and use the Multiplication Property of Square Roots. = 21 4x2 • 10 4x2 is a perfect square and a factor of 40x2. = 21 4x2 • 10 Use the Multiplication Property of Square Roots. = 21 • 2x 10 Simplify 4x2. = 42x 10 Simplify. 11-1

The distance you can see is 9 miles. ALGEBRA 1 LESSON 11-1 Suppose you are looking out a fourth floor window 54 ft above the ground. Use the formula d = 1.5h to estimate the distance you can see to the horizon. d = 1.5h = 1.5 • 54 Substitute 54 for h. = 81 Multiply. = 9 Simplify 81. The distance you can see is 9 miles. 11-1

Simplify each radical expression. ALGEBRA 1 LESSON 11-1 Simplify each radical expression. a. 13 64 b. 49 x4 = Use the Division Property of Square Roots. 13 64 = Simplify 64. 13 8 = Use the Division Property of Square Roots. 49 x4 7 x2 = Simplify 49 and x4. 11-1

Simplify each radical expression. ALGEBRA 1 LESSON 11-1 Simplify each radical expression. a. 120 10 = 12 Divide. 120 10 = 4 • 3 4 is a perfect square and a factor of 12. = 4 • 3 Use the Multiplication Property of Square Roots. = 2 3 Simplify 4. 11-1

= Divide the numerator and denominator by 3x. ALGEBRA 1 LESSON 11-1 (continued) b. 75x5 48x = Divide the numerator and denominator by 3x. 75x5 48x 25x4 16 = Use the Division Property of Square Roots. 25x4 16 = Use the Multiplication Property of Square Roots. 25 • x4 16 = Simplify 25, x4, and 16. 5x2 4 11-1

Simplify each radical expression. ALGEBRA 1 LESSON 11-1 Simplify each radical expression. a. 3 7 3 7 = • Multiply by to make the denominator a perfect square. = Use the Multiplication Property of Square Roots. 3 7 49 = Simplify 49. 3 7 7 11-1

Simplify the radical expression. ALGEBRA 1 LESSON 11-1 (continued) Simplify the radical expression. b. 11 12x3 = • Multiply by to make the denominator a perfect square. 3x 11 12x3 = Use the Multiplication Property of Square Roots. 33x 36x4 = Simplify 36x4. 33x 6x2 11-1

Summary: Don’t forget to write your minimum three sentence summary answering today’s essential question here!