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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? 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. ALGEBRA 1 LESSON 11-1 Simplify 243 = = =9 243. 81 • 3 81 is a perfect square and a factor of 243. 81 • Use the Multiplication Property of Square Roots. 3 3 Simplify 81. 11-1 ALGEBRA 1 LESSON 11-1 Simplify 4x6 • 7x 28x7 = = 4x6 • = 2x3 7x 7x 28x7. 4x6 is a perfect square and a factor of 28x7. Use the Multiplication Property of Square Roots. Simplify 4x6. 11-1 ALGEBRA 1 LESSON 11-1 Simplify each radical expression. a. 12 • 12 • 32 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 • = 8 6 6 Use the Multiplication Property of Square Roots. Simplify 11-1 64. 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 factor of 40x2. 4x2 is a perfect square and a = 21 4x2 • 10 Square Roots. Use the Multiplication Property of = 21 • 2x Simplify = 42x 10 10 Simplify. 11-1 4x2. 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 ALGEBRA 1 LESSON 11-1 Simplify each radical expression. a. b. 13 64 13 = 64 13 64 Use the Division Property of Square Roots. = 13 8 Simplify 49 = x4 49 x4 Use the Division Property of Square Roots. 64. 49 x4 7 = x2 Simplify 49 and 11-1 x4. ALGEBRA 1 LESSON 11-1 Simplify each radical expression. a. 120 10 120 = 10 12 Divide. = 4•3 4 is a perfect square and a factor of 12. = 4• =2 3 3 Use the Multiplication Property of Square Roots. Simplify 11-1 4. ALGEBRA 1 LESSON 11-1 (continued) b. 75x5 48x 75x5 = 48x 25x4 16 = 25x4 16 = = 25 • 16 5x2 4 Divide the numerator and denominator by 3x. Use the Division Property of Square Roots. x4 Use the Multiplication Property of Square Roots. Simplify 25, 11-1 x4, and 16. ALGEBRA 1 LESSON 11-1 Simplify each radical expression. a. 3 7 3 = 7 = = 3 • 7 7 7 Multiply by 7 7 to make the denominator a perfect square. 3 7 49 3 7 7 Use the Multiplication Property of Square Roots. Simplify 11-1 49. ALGEBRA 1 LESSON 11-1 (continued) Simplify the radical expression. b. 11 12x3 11 = 12x3 11 • 12x3 3x 3x = 33x 36x4 Use the Multiplication Property of Square Roots. = 33x 6x2 Simplify Multiply by 3x to make the denominator a 3x perfect square. 11-1 36x4. Summary: Don’t forget to write your minimum three sentence summary answering today’s essential question here!