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Solution to BOP:

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.

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Solution to BOP:

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

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

  3. Prentice Hall Lesson 11.1How 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.

  4. 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.

  5. 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.

  6. 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

  7. ALGEBRA 1 LESSON 11-1 Simplify 28x7. 28x7 = 4x6 • 7x4x6 is a perfect square and a factor of 28x7. = 4x6 • 7xUse the Multiplication Property of Square Roots. = 2x3 7x Simplify 4x6. 11-1

  8. ALGEBRA 1 LESSON 11-1 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. Simplify each radical expression. 11-1

  9. ALGEBRA 1 LESSON 11-1 7 5x • 3 8x = 21 40x2Multiply 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. (continued) b. 7 5x • 3 8x 11-1

  10. 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 • 54Substitute 54 for h. = 81 Multiply. = 9 Simplify 81. The distance you can see is 9 miles. 11-1

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

  12. ALGEBRA 1 LESSON 11-1 120 10 a. 120 10 = 12 Divide. = 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. Simplify each radical expression. 11-1

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

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

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

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

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